Area and Volume Unit Test
4 of 154 of 15 Items
Question
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)
in.2
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To find the area of the quadrilateral, we can divide it into two triangles and find the area of each triangle separately.
The area of a triangle is given by the formula: area = 1/2 * base * height
First, let's find the area of the triangle on the left side of the parallelogram:
base = 12 inches
height = 16 inches
area = 1/2 * 12 * 16
area = 96 square inches
Now, let's find the area of the triangle on the right side of the parallelogram:
base = 12 inches
height = 16 inches
area = 1/2 * 12 * 16
area = 96 square inches
Since the area of the quadrilateral is the sum of the areas of the two triangles, we can find the total area:
total area = 96 + 96
total area = 192 square inches
Therefore, 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
68 square units
68 square units
77 square units
77 square units
83 square units
83 square units
72 square units
To find the area of the polygon, we will divide it into two rectangles and a square and then add their areas together.
First, let's find the area of the rectangle on the left side of the polygon:
Length = 12 units
Width = 3 units
Area = Length * Width = 12 * 3 = 36 square units
Next, let's find the area of the rectangle on the right side of the polygon:
Length = 12 units
Width = 3 units
Area = Length * Width = 12 * 3 = 36 square units
Now, let's find the area of the square in the middle of the polygon:
Side length = 5 units
Area = Side length^2 = 5^2 = 25 square units
Adding the areas of the two rectangles and the square:
Total area = 36 + 36 + 25 = 97 square units
Therefore, the area of the polygon is 97 square units. The closest option provided is 83 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)
square feet
Since we are instructed to compose a rectangle to find the area of the pool, we can consider the parallelogram as a rectangle since the opposite sides of a parallelogram are equal in length.
Therefore, the base of the parallelogram (12 feet) becomes the base of the rectangle and the perpendicular height (7 inches) from the top left vertex to the base becomes the height of the rectangle.
To find the area of the rectangle (and hence the parallelogram), we use the formula for the area of a rectangle: Area = Length x Width.
Converting the height from inches to feet for consistency, we have: 7 inches = 7/12 feet.
Height = 7/12 feet
Base = 12 feet
Area = Base x Height
Area = 12 feet x 7/12 feet
Area = 84/12 square feet
Area = 7 square feet
Therefore, the area of the pool, and by extension the parallelogram-shaped swimming pool, is 7 square feet.
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)
square inches
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To find the total area of the shape representing the unfolded box net, we need to find the areas of the individual polygons and then add them up.
First, let's find the area of the rectangle in the center:
Width = 6 + 3 + 3 = 12 inches
Height = 1 inch (since the dotted lines are not used in the rectangle's height)
Area of rectangle = 12 * 1 = 12 square inches
Next, let's find the area of the trapezoid on the left:
Base 1 = 3 inches
Base 2 = 6 inches
Height = 1 inch
Area of trapezoid = (1/2) * (Base 1 + Base 2) * Height
Area of trapezoid = (1/2) * (3 + 6) * 1
Area of trapezoid = 4.5 square inches
Now, let's find the area of the trapezoids on the top and bottom:
Since they are congruent trapezoids, we only need to calculate one.
Top and bottom base length = 12 inches (length of the rectangle)
Shorter base = 3 inches
Height = 1.2 inches
Area of trapezoid = (1/2) * (Base 1 + Base 2) * Height
Area of trapezoid = (1/2) * (3 + 12) * 1.2
Area of trapezoid = 7.8 square inches
Finally, adding up the areas of all the polygons:
Total area = Rectangle area + Left trapezoid area + 2 * Top or Bottom trapezoid area
Total area = 12 + 4.5 + 2 * 7.8
Total area = 12 + 4.5 + 15.6
Total area = 32.1 square inches
Therefore, the area of the shape representing the unfolded box net is 32.1 square inches.
Use the image to answer the question.
An illustration shows an outline of a right arrow consisting of a rectangle and a triangular head to its right. The length of the rectangle is 4 and the width is 2. The right width of the triangle does not show a line. It forms the central part of the verticle base of the triangle. The other parts of the base are labeled 2 on the top and bottom each. The perpendicular height from the base to the top vertex of the triangle is labeled as 5.
An artist is planning to paint an arrow using the pattern shown. What is the amount of area in square feet that will be painted?
(1 point)
square feet
To find the total area of the right arrow shape, we need to find the areas of the rectangle and the triangle, and then add them together.
First, let's find the area of the rectangle:
Length = 4 feet
Width = 2 feet
Area of rectangle = Length x Width = 4 x 2 = 8 square feet
Next, let's find the area of the triangle:
Base of the triangle:
Top part = 2 feet
Bottom part = 2 feet
Central part (missing length) = 4 - 2 - 2 = 0 feet
Since the height of the triangle is given as 5 feet and we are given the vertical base lengths, we can see that the triangle is a right triangle with base 4 (2 + 2) and height 5. Therefore, the triangle area is:
Area of triangle = 1/2 x base x height = 1/2 x 4 x 5 = 10 square feet
Total area painted = Area of rectangle + Area of triangle = 8 + 10 = 18 square feet
Therefore, the amount of area that will be painted in square feet is 18 square feet.
se 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)
cm3