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.

Answer 1

Option C : $148 in ^{2}$ is the area of the trapezoid.

Explanation:

The measurements of this trapezoid is attached in the image given below:

The formula to find the area of the trapezoid is given by

$A=\frac{1}{2}(a+b) h$

where a and b are the base

h is the height of the trapezoid.

From the figure, the value of the bases a and b are

$a=A B=14$

$b=D F+F E+E C\\b =3+14+6=23$

$h=EB=8$

Now, substituting these values in the area of the trapezoid, we get,

$A=\frac{1}{2}(14+23) 8$

$A=\frac{1}{2}(37) 8$

$A=148 in^2$

Therefore, the area of the trapezoid is $A=148 in^2$

Hence, Option C is the correct answer.