What is the area of the quadrilateral?

Question

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

Answer 1

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.

Answer 2

No trapezoids

Answer 3

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.