A rectangular poster has a length of 72 centimeters and a width of 15 centimeters. The poster is reduced in size by 6 centimeters in length and 3 centimeters in width. What is the area of the new poster?
The area of the original poster is:
72 cm x 15 cm = 1080 cm²
After reducing the length by 6 cm and the width by 3 cm, the new dimensions are:
(72 cm - 6 cm) x (15 cm - 3 cm) = 66 cm x 12 cm
The area of the new poster is:
66 cm x 12 cm = 792 cm²
Therefore, the area of the new poster is 792 square centimeters.
The area of a right triangle is (base x height)/2.
Plugging in the given measurements, we get:
Area = (4.25 in x 11 in)/2 = 23.375 square inches
Therefore, the area of the right triangle is 23.375 square inches.
Use the image to answer the question.
An illustration shows a 10 by 10 grid. A non-right triangle is enclosed within the grid. The first vertex is at the top of row 2 and the right of column 6. The second vertex is at the top of row 8 and the right of column 1. The third vertex is at the top of row 10 and right of column 10.
What is the area of the non-right triangle? The base and height are found by counting the squares.
(1 point)
We can find the base and height of the triangle by counting the number of squares in each direction.
The base has 6 squares going to the right, and the height has 3 squares going down.
Using the formula for the area of a triangle (A = 1/2 x base x height), we get:
A = 1/2 x 6 x 3 = 9 square units
Therefore, the area of the non-right triangle is 9 square units.
A piece of paper is in the shape of a right triangle. The base is 4.25 inches and the height is 11 inches. What is the area of the right triangle in square inches?
Use the image to answer the question.
An illustration shows a parallelogram with the right side as 16 inches. A perpendicular dotted line from top right vertex to the left side is 12 inches. The perpendicular line makes one right angle symbol with right side and two right angle symbols with the left side.
What is the area of the quadrilateral?
(1 point)
We can find the area of the quadrilateral by multiplying the base (the length of the right side, which is 16 inches) by the height (the length of the dotted line, which is 12 inches).
Therefore, the area of the quadrilateral is:
16 inches x 12 inches = 192 square inches
So, the area of the quadrilateral is 192 square inches.
Use the image to answer the question.
An illustration shows the outline of letter upper H. The two vertical sides of the outline letter upper H have length 12 and width 3. The horizontal part across the middle has length 5. The inner side of the upper vertical part of the H has length 5. The inner side of the lower vertical part has length 6.
What is the area of the polygon?
(1 point)
Responses
72 square units
72 square units
68 square units
68 square units
83 square units
83 square units
77 square units
77 square units
Use the image to answer the question.
An illustration of a parallelogram shows the following dimensions: The base is 12 feet. The perpendicular height from the top left vertex to the base is 7 inches. The height is drawn as a dashed line.
A pool company is installing a parallelogram-shaped swimming pool in a family’s back yard. Compose a rectangle to find the amount of area that the pool will take up in the yard. What is the area of the pool?
(1 point)
Use the image to answer the question.
An illustration of a parallelogram shows the following dimensions: The base is 12 feet. The perpendicular height from the top left vertex to the base is 7 inches. The height is drawn as a dashed line.
A pool company is installing a parallelogram-shaped swimming pool in a family’s back yard. Compose a rectangle to find the amount of area that the pool will take up in the yard. What is the area of the pool?
(1 point)
Area and Volume Unit Test
7 of 157 of 15 Items
Question
Use the image to answer the question.
An illustration shows an unfolded box net. It is comprised of a rectangle at the center, two squares extending into three trapezoids on the top and bottom, and a trapezoid on the left of the rectangle. The top side of the rectangle is labeled in three distinct sections: starting at the left, a solid line of 3 is drawn, followed by a dashed line of 3, and then a solid line of 6. The bottom of the rectangle is labeled in three distinct sections: a solid line of 6, a dashed line of 3, and a solid line of 3. The left width of the rectangle is drawn as a dashed line, labeled as 3, which becomes the base of a shaded trapezoid. The dashed lines on the top and bottom of the rectangle are extended into squares of side 3, sides drawn in dashed lines. The three outer sides of each square become the longer bases of shaded trapezoids. The top shorter side of the trapezoid is labeled as 1.2 and the perpendicular height is 1.
Decompose the box net into simple polygons to find how much cardboard in square inches is needed to make the cube. Assume that all angles that look like right angles are right angles. All polygons that look congruent are congruent. What is the area of the shape in square inches?
(1 point)
Use the image to answer the question.
An illustration shows a rectangular prism. The top, front, and right faces are visible. The edges that are not visible are indicated by a dashed line. The base is labeled upper B equals 240 centimeters squared. The bottom front edge is labeled l equals 24 centimeters. A vertical edge is labeled h equals 8 centimeters.
Find the volume of the right rectangular prism.
(1 point)
Use the image to answer the question.
An illustration shows a vertical rectangular prism made of cubes placed as two columns, each 5 cubes high.
What is the volume of the right rectangular prism packed with 10 cubes? Each cube has an edge length of 13 meter.
(1 point)
Responses
10 cubic meters
, 10 cubic meters
127 cubic meters
, Start Fraction 1 over 27 End Fraction, cubic meters
103 cubic meters
, Start Fraction 10 over 3 End Fraction, cubic meters
1027 cubic meters
Start Fraction 10 over 27 End Fraction, cubic meters
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Area and Volume Unit Test
11 of 1511 of 15 Items
Question
Use the image to answer the question.
An illustration shows a 3 D rectangular cuboid segmented into 5 rows by 2 columns of blocks. The length is start fraction 1 over 2 end fraction, width is start fraction 1 over 4 end fraction, and height is start fraction 5 over 4 end fraction.
Multiply the edge lengths of a right rectangular prism with length 12 m, width 14 m, and height 54 m to show that the product is the same as the volume found by packing the prism with 10 unit cubes with an edge length of 14 m. What is the volume of the prism?
(1 point)
What is the volume of a rectangular prism with a length of 423 ft., a height of 313 ft., and a width of 212 ft.?(1 point)
What is the volume of a rectangular prism with a length of 4/23 ft., a height of 3/13 ft., and a width of 2/12 ft.?(1 point)
In cubic feet, what is the volume of a toy box measuring 3 3/4 feet long, 2 1/2 feet wide, and 2 1/2 feet tall? Use the volume formula to solve. The answer will be a mixed fraction in cubic feet.(1 point)
To find the area of the net, we need to calculate the area of each of the simple polygons and then add them together.
Starting with the rectangle in the center, the area is:
6 inches x 6 inches = 36 square inches
For each of the four trapezoids surrounding the rectangle, we can split each one into a rectangle and two right triangles and then add together the areas of those three shapes. The area of a rectangle is base x height, and the area of a right triangle is 1/2 x base x height.
The trapezoid on the left has a height of 3 inches and bases of 3 inches and 6 inches. Therefore, its area is:
(3 inches + 6 inches) / 2 x 3 inches = 13.5 square inches
Each of the four trapezoids on the top and bottom has a height of 1 inch and bases of 3 inches, 3 inches, and 6 inches. Therefore, each trapezoid’s area is:
(3 inches + 3 inches) / 2 x 1 inch + 6 inches x 1 inch = 6.5 square inches
Since there are four such trapezoids, their combined area is:
4 x 6.5 square inches = 26 square inches
Each of the two squares has a side length of 3 inches, so each square’s area is:
3 inches x 3 inches = 9 square inches
The four trapezoids formed by extending the sides of each square have heights of 1 inch, shorter bases of 3 inches, and longer bases of 4.2 inches (since 3 inches + 1.2 inches = 4.2 inches). Therefore, the area of a trapezoid is:
(3 inches + 4.2 inches) / 2 x 1 inch = 3.6 square inches
Since there are four such trapezoids, their combined area is:
4 x 3.6 square inches = 14.4 square inches
Finally, the shaded trapezoid on the left has a height of 6 inches (since it is on the side of the cube), a shorter base of 3 inches, and a longer base of 4.2 inches. Therefore, its area is:
(3 inches + 4.2 inches) / 2 x 6 inches = 22.8 square inches
Adding together the areas of all the simple polygons, we get:
36 square inches + 13.5 square inches + 26 square inches + 9 square inches + 14.4 square inches + 22.8 square inches = 122.7 square inches
Therefore, the area of the net is 122.7 square inches.
To find the volume of the rectangular prism, we need to multiply its length, width, and height.
From the image, we can see that the length of the rectangular prism is not labeled, but it is perpendicular to the front edge labeled l and the vertical edge labeled h. Therefore, the length is the third dimension (besides height and width) that defines the rectangular prism.
The area of the base, which is the product of length and width, is given as 240 square centimeters. So we can find the length by dividing the area of the base by the width.
240 square centimeters ÷ width = length
We also know that the front edge labeled l has a length of 24 centimeters, so we can use this to find the width.
Using the Pythagorean theorem, we can see that the front edge l, the vertical edge h, and the diagonal edge that connects them form a right triangle. Therefore, we can find the width as the square root of the difference between the diagonal and the vertical edge squared:
width = √(l² - h²) = √((24 cm)² - (8 cm)²) = √(576 cm² - 64 cm²) = √512 cm ≈ 22.63 cm
Now that we know the width and length, we can find the volume of the rectangular prism:
Volume = length x width x height = (240 cm² ÷ width) x width x 8 cm = 1920 cm³
Therefore, the volume of the rectangular prism is 1920 cubic centimeters.
Each column of the rectangular prism is 5 cubes high, so the height of the rectangular prism is 10 cubes high. Each cube has an edge length of 13 meters.
To find the volume of the rectangular prism, we need to multiply its length, width, and height. From the image, we can count that the length of the rectangular prism is 2 cubes long (since it has two columns of 5 cubes each), and the width is 1 cube wide.
Therefore, the volume of the rectangular prism is:
length x width x height = 2 cubes x 1 cube x 10 cubes = 20 cubic units
Since each cube has an edge length of 13 meters, the unit for volume is cubic meters. Therefore, the volume of the rectangular prism is:
20 cubic units x (13 meters)³ = 35,420 cubic meters
So, the volume of the right rectangular prism packed with 10 cubes is 35,420 cubic meters.
The length of the right rectangular prism is 12 meters, the width is 14 meters, and the height is 54 meters. Therefore, the volume of the prism is:
Volume = length x width x height = 12 m x 14 m x 54 m = 9072 cubic meters
If we pack the prism with 10 unit cubes with an edge length of 14 meters, then the number of cubes needed to fill the prism is the volume of the prism divided by the volume of one cube:
number of cubes = Volume of prism / Volume of one cube = 12 m x 14 m x 54 m / (14 m)³ = 540
The volume of each cube is:
length x width x height = (14 m) x (14 m) x (14 m) = 2744 cubic meters
So, the total volume of the 540 cubes is:
Volume of 540 cubes = 540 x 2744 cubic meters = 1,482,960 cubic meters
Now, we can multiply the edge lengths of the right rectangular prism to show that the product is the same as the volume found by packing the prism with 10 unit cubes:
length x width x height = 12 m x 14 m x 54 m = (2 x 6 m) x (4 x 3.5 m) x (5 x 4.5 m) = 10 x (0.5 m x 1 m x 2 m) x (0.25 m x 1 m x 2 m) x (1.25 m x 1 m x 2 m)
This is the same as packing the prism with 10 unit cubes that have dimensions of 0.5 m x 0.25 m x 1.25 m. So we can find the volume by multiplying the number of cubes by the volume of one cube:
Volume = Number of cubes x Volume of one cube = 10 x (0.5 m x 0.25 m x 1.25 m) = 1.5625 cubic meters
Therefore, the volume of the right rectangular prism packed with 10 unit cubes is the same as the volume of the prism itself:
9072 cubic meters = 1.5625 cubic meters
So, the volume of the prism is 9072 cubic meters.
The volume of a rectangular prism is given by the formula:
Volume = length x width x height
Plugging in the given measurements, we have:
Volume = 423 ft. x 212 ft. x 313 ft. = 28,263,084 cubic feet
Therefore, the volume of the rectangular prism is 28,263,084 cubic feet.
We can see that the polygon can be divided into three smaller rectangles and two smaller squares.
The first rectangle has a length of 12 units and a width of 3 units, so its area is:
12 units x 3 units = 36 square units
The second rectangle has a length of 12 units and a width of 3 units, so its area is also 36 square units.
The two squares have sides of length 5 units and 6 units, so their areas are:
5 units x 5 units = 25 square units
6 units x 6 units = 36 square units
Finally, the third rectangle has a length of 5 units and a width of 11 units (12 units minus the 1 unit overlap in the middle), so its area is:
5 units x 11 units = 55 square units
Adding up the areas of all the individual shapes, we get:
36 square units + 36 square units + 25 square units + 36 square units + 55 square units = 188 square units
Therefore, the area of the polygon is 188 square units.
The pool is in the shape of a parallelogram, which means its opposite sides are parallel. Therefore, we can draw a rectangle with the same base (12 feet) as the parallelogram and the same height (7 inches) as the perpendicular height of the parallelogram.
To convert the height of the parallelogram from 7 inches to feet, we divide by 12 (since there are 12 inches in a foot):
7 inches ÷ 12 = 0.58 feet
So the height of the rectangle is 0.58 feet.
The area of the parallelogram is the same as the area of the rectangle, which is:
base x height = 12 feet x 0.58 feet = 6.96 square feet
Therefore, the area of the pool is 6.96 square feet.
The pool is in the shape of a parallelogram, which means its opposite sides are parallel. Therefore, we can draw a rectangle with the same base (12 feet) as the parallelogram and the same height (7 inches) as the perpendicular height of the parallelogram.
To convert the height of the parallelogram from 7 inches to feet, we divide by 12 (since there are 12 inches in a foot):
7 inches ÷ 12 = 0.58 feet
So the height of the rectangle is 0.58 feet.
The area of the parallelogram is the same as the area of the rectangle, which is:
base x height = 12 feet x 0.58 feet = 6.96 square feet
Therefore, the area of the pool is 6.96 square feet.