Does anyone have the answers to the surface area and volume unit test
Unit 6 lesson 10 for connexus
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?(1 point)
The area of the original poster is:
A1 = length × width
A1 = 72 cm × 15 cm
A1 = 1080 cm²
The length of the new poster is 72 cm - 6 cm = 66 cm, and the width is 15 cm - 3 cm = 12 cm.
The area of the new poster is:
A2 = length × width
A2 = 66 cm × 12 cm
A2 = 792 cm²
Therefore, the area of the new poster is 792 cm².
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?
The area of the right triangle is:
A = (base × height) / 2
A = (4.25 in × 11 in) / 2
A = 23.375 in²
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.
To find the area of the non-right triangle, we need to first find its base and height using the grid.
The base of the triangle is the horizontal distance between the second vertex (top of row 8, right of column 1) and the third vertex (top of row 10, right of column 10). From the grid, we can count that there are 8 squares between these two vertices horizontally.
The height of the triangle is the vertical distance between the first vertex (top of row 2, right of column 6) and a line passing through the third vertex and parallel to the base. Since the third vertex is at the top of row 10, we count 8 squares vertically to find the height.
So the area of the non-right triangle is:
A = (base × height) / 2
A = (8 squares × 8 squares) / 2
A = 32 squares
Each square on the grid has an area of 1, so the area of the non-right triangle is 32 square units.
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?
To find the area of the quadrilateral, we need to first find the height of the parallelogram. The perpendicular dotted line from the top right vertex to the left side has a length of 12 inches and forms a right angle with the left side of the parallelogram. This means that the left side is the base of the parallelogram and the length of the dotted line is the height.
So the area of the parallelogram is:
A = base × height
A = 16 in × 12 in
A = 192 in^2
However, the quadrilateral is not a parallelogram but it is still made up of two right triangles. We can see that the dotted line from the top right vertex to the left side of the parallelogram divides it into two right triangles. The area of each of these triangles is:
A = (base × height) / 2
For the left triangle, the base is 12 inches (the dotted line) and the height is 16 inches, so:
A = (12 in × 16 in) / 2
A = 96 in^2
For the right triangle, the base is 12 inches (the dotted line) and the height is also 12 inches (the distance from the top right vertex to the dotted line), so:
A = (12 in × 12 in) / 2
A = 72 in^2
Therefore, the area of the quadrilateral is the sum of the areas of the two triangles:
A = 96 in^2 + 72 in^2
A = 168 in^2
So the area of the quadrilateral is 168 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)
83 square units
68 square units
72 square units
77 square units
To find the area of the polygon, we need to break it down into simpler shapes and calculate their areas separately. We can see that the polygon is made up of two rectangles and two right triangles.
The first rectangle is the one in the middle, with a length of 5 units and a width of 3 units. Its area is:
A1 = length × width
A1 = 5 units × 3 units
A1 = 15 square units
The second rectangle is one of the vertical sides, with a length of 12 units and a width of 3 units. Its area is:
A2 = length × width
A2 = 12 units × 3 units
A2 = 36 square units
To find the areas of the two right triangles, we need to first find their base and height. The base of each triangle is the difference between the length of the inner side and the width of the polygon. The height of each triangle is the same as the length of the vertical sides.
For the first triangle (on the left), the base is:
base = (length of inner side) - (width of polygon)
base = 5 units - 3 units
base = 2 units
The height is 12 units (the length of the vertical side).
So the area of the first triangle is:
A3 = (base × height) / 2
A3 = (2 units × 12 units) / 2
A3 = 12 square units
For the second triangle (on the right), the base is:
base = (length of inner side) - (width of polygon)
base = 6 units - 3 units
base = 3 units
The height is also 12 units.
So the area of the second triangle is:
A4 = (base × height) / 2
A4 = (3 units × 12 units) / 2
A4 = 18 square units
Finally, we can find the total area of the polygon by adding up the areas of all the shapes:
A = A1 + A2 + A3 + A4
A = 15 square units + 36 square units + 12 square units + 18 square units
A = 81 square units
Therefore, the area of the polygon is 81 square units. None of the given options match the answer.