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
648 square inches
648 square inches
864 square inches
864 square inches
756 square inches
756 square inches
882 square inches
756 square inches
To find the area of the trapezoid-shaped tabletop, we can use the formula A = (b1 + b2)h/2, where b1 and b2 are the lengths of the two bases and h is the perpendicular height between them.
First, we can use the given information to label the trapezoid's dimensions:
- Shorter base: b1 = 36
- Longer base: b2 = 48
- Legs: 21
- Perpendicular height: h = 18
- Length from top left vertex to point where height meets longer side: 6
Next, we can use this information to compose a rectangle by extending the shorter base to meet the longer base and drawing a line parallel to the bases to connect the leg endpoints. This rectangle has dimensions:
- Length: 48
- Height: 21+18+6 = 45 (summing the lengths of the legs, height, and length from top left vertex to point where height meets longer side)
The trapezoid occupies half of this rectangle, so its area can be found by dividing the area of the rectangle by 2:
A = (48*45)/2 = 1080
But we only want the area of the trapezoid-shaped tabletop, not the entire rectangle. To find this, we can subtract the area of the right triangle protruding from the top right corner of the trapezoid:
A(trapezoid) = A(rectangle)/2 - A(triangle)
A(trapezoid) = 1080/2 - (1/2)(6)(21)
A(trapezoid) = 540 - 63
A(trapezoid) = 477
Therefore, the area of the trapezoid-shaped tabletop is 477 square inches.
Use Area to Solve Problems Quick Check
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
648 square inches
648 square inches
864 square inches
864 square inches
882 square inches
882 square inches
756 square inches
756 square inches
The area of the trapezoid-shaped tabletop is 477 square inches.
the options are 648 sq in, 864 sq in, 882 sq in, and 756 sq in....o-o
I apologize for the error. The correct answer is 756 square inches.
It's okay to not get a perfect score on a quick check. What's important is that you understand the concepts and learn from any mistakes you made. Don't hesitate to seek help or ask questions if you need further clarification or assistance. Keep practicing, and you'll continue to improve.
To find the area of the trapezoid-shaped tabletop, we can use the formula for the area of a trapezoid:
Area = (base1 + base2) * height / 2
In the given illustration, we are given the dimensions of the trapezoid. The shorter base (base1) is labeled as 36 inches, and the opposite longer side (base2) is labeled as 48 inches. The height of the trapezoid is given as 18 inches.
To compose a rectangle to help find the area, we can create a rectangle that has the same base, base1, and height as the trapezoid. In this case, the base of the rectangle will be 36 inches, and the height will be 18 inches.
Using the formula for the area of a rectangle:
Area = base * height
Area = 36 inches * 18 inches
Area = 648 square inches
Therefore, the area of the trapezoid-shaped tabletop is 648 square inches.
756
128
480
12 & 12
1.99
TRUST ME
step by step explanation of: 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
648 square inches
648 square inches
864 square inches
864 square inches
882 square inches
882 square inches
756 square inches
756 square inches
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