Question

What is the area of this trapezoid?

86 in²

112 in²

148 in²

184 in²
Trapezoid A B C D with parallel sides D C and A B. Point F and E are on side D C. Point F is connected to point A by a dotted segment. Point E is connected to point B by a dotted segment. A B E F is a rectangle. D F is 3 inches. E C is 6 inches. E B is 8 inches. A B is 14 inches. god i need help

Answer 1

Area of the trapezoid = 148 inch²

Solution:

Base of the bottom side (AB) = 14 in

Base of the top side (DC) = DF + FE + EC

= 3 in + 14 in + 6 in

= 23 inch

Height of the trapezoid (BE) = 8 in

Parallel sides of the trapezoid are DC and AB.

To find the area of the trapezoid:

Area of the trapezoid =
`(1)/(2)* \text{Sum of the parallel sides}* \text{Height}`

`$=(1)/(2)*({DC+AB})*{BE}`

`$=(1)/(2)*{(23+14)}*{8}`

`$=(1)/(2)*{37}*{8}`

`$=148`

Area of the trapezoid = 148 inch