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: $148 \mathrm{in}^{2}$ is the area of the trapezoid.

Explanation:

The image of the trapezoid having these descriptions is attached below:

Now, we shall determine the area of the trapezoid using the formula,

$A=\frac{a+b}{2} h$ where a and b are the base of the trapezoid and h is the height of the trapezoid.

Thus, we shall find the value of a and b from the diagram given below.

$a= AB=14in$

$b=DC\\b=DF+FE+EC\\b=3+14+6\\b=23in$

It is given that the height of the trapezoid $h=8in$

Thus, substituting the values of a,b and h in the formula $A=\frac{a+b}{2} h$, we get,

$A=\frac{14+23}{2}(8)\\ A=\frac{37}{2} (8)\\A=148in^2$

Thus, the area of the trapezoid is $148 \mathrm{in}^{2}$

Hence, Option C is the correct answer.