Use Area to Solve Problems Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Use the image to answer the question.
An illustration shows a parallelogram with a base length of 12 meters and right side of 10 meters.
A gardener wants to cover a parallelogram-shaped piece of land with colorful flowers. To find the area of the garden, the gardener composes a rectangle. What is the base of the rectangle in meters?
(1 point)
meters
The base of the rectangle would be the same as the base of the parallelogram, which is 12 meters.
Use Area to Solve Problems Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows a parallelogram that is divided into four equal sections by a horizontal and a vertical line intersecting at the center. Measurements are labeled on the bottom first section as follows: The base is labeled 8 inches and left side is 5 inches. The perpendicular height from the top left vertex to the base is 4 inches. The height is drawn in dashed line.
To cover a garden path, a landscape designer plans to cover a walkway with parallelogram-shaped paving stones. Construct a rectangle to find the area covered by 4 paving stones. What is the area in square inches?
(1 point)
Responses
52 square inches
52 square inches
160 square inches
160 square inches
128 square inches
128 square inches
40 square inches
To find the area covered by 4 paving stones, we first need to find the area of one paving stone. The given parallelogram has a base of 8 inches and a height of 4 inches (perpendicular height from the top left vertex to the base), so the area of one paving stone would be 8 * 4 = 32 square inches.
Since there are 4 paving stones, the total area covered by 4 paving stones would be 4 * 32 = 128 square inches.
Therefore, the area covered by 4 paving stones is 128 square inches.
The correct response is:
128 square inches
this counts towards my grade if its wrong its because you give me the wrong answer
Understood! If this is a graded assessment and you have any specific questions you'd like help with or need clarification on, feel free to ask. I'm here to assist you.
okay here is my first one Use the image to answer the question.
An illustration shows a trapezoid with shorter base of length 36 and the opposite longer side of length 48. The legs on the left and right sides are of length 21. The perpendicular height from the bottom left vertex to the longer side is 18. The length between the top left vertex of the longer side and the point where the height meets the longer side is labeled 6. The height is shown in a dashed line.
Compose a rectangle to help find the area of a trapezoid-shaped tabletop in square inches. What is the area of the tabletop?
(1 point)
Responses
756 square inches
756 square inches
648 square inches
648 square inches
882 square inches
882 square inches
864 square inches
To find the area of the trapezoid-shaped tabletop, we first need to find the height of the trapezoid. From the information given, the height of the trapezoid is considered to be the perpendicular height from the bottom left vertex to the longer side, which is 18 inches.
Now, we can split the trapezoid into a rectangle and a right-angled triangle by drawing a horizontal line from the top left vertex of the longer side where the height meets, forming a right triangle with dimensions 6, 18, and 21 inches.
The area of the rectangle is base * height = 36 * 18 = 648 square inches.
The area of the right-angled triangle is 0.5 * 6 * 18 = 54 square inches.
Therefore, the total area of the trapezoid-shaped tabletop would be the sum of the area of the rectangle and the area of the right-angled triangle: 648 + 54 = 702 square inches.
So, the correct response is:
756 square inches
you sure
Apologies for the mistake in the previous response. Let's correct that calculation:
To find the area of the trapezoid-shaped tabletop:
1. Divide the trapezoid into a rectangle and a right triangle by drawing a horizontal line from the top left vertex of the longer side to where the height meets:
- The rectangle has an area of base * height = 36 * 18 = 648 square inches.
- The right triangle has an area of 0.5 * base * height = 0.5 * 6 * 18 = 54 square inches.
Adding the areas of the rectangle and the right triangle: 648 (rectangle) + 54 (triangle) = 702 square inches.
Therefore, the correct response should be:
702 square inches