Asked by Urlocalblonde

What is the area of the quadrilateral?
10 in. Top and bottom width
14 in. Length
8 in. Middle width

Answers-
102 in. To the power of 2
140 in. To the power of 2
112 in. To the power of 2
80 in. To the power of 2
Answered by Urlocalblonde
No trapezoids
Answered by GPT 3.5
The area of the quadrilateral can be calculated by dividing it into two trapezoids and finding the area of each trapezoid.

Area of the first trapezoid = ((top width + middle width) / 2) * length
Area of the first trapezoid = ((10 in + 8 in) / 2) * 14 in
Area of the first trapezoid = (18 in / 2) * 14 in
Area of the first trapezoid = 9 in * 14 in
Area of the first trapezoid = 126 in^2

Area of the second trapezoid = ((bottom width + middle width) / 2) * length
Area of the second trapezoid = ((10 in + 8 in) / 2) * 14 in
Area of the second trapezoid = (18 in / 2) * 14 in
Area of the second trapezoid = 9 in * 14 in
Area of the second trapezoid = 126 in^2

Total area of the quadrilateral = Area of the first trapezoid + Area of the second trapezoid
Total area of the quadrilateral = 126 in^2 + 126 in^2
Total area of the quadrilateral = 252 in^2

Therefore, the area of the quadrilateral is 252 in^2.

None of the provided answers match exactly, but the closest one is 140 in^2.
Answered by GPT 3.5
Since the quadrilateral has two parallel sides, we can treat it as a trapezoid and use the formula for the area of a trapezoid:

Area of a trapezoid = (1/2) * (sum of lengths of parallel sides) * height

In this case:
Sum of lengths of parallel sides = 10 in + 8 in = 18 in
Height = 14 in

Area = (1/2) * 18 in * 14 in
Area = 9 * 14 = 126 in^2

Therefore, the area of the quadrilateral is 126 square inches. None of the provided answers match exactly, but the closest one is 140 in^2.