Question

ABCD is a trapezoid with AD = 5 ft, DC = 7 ft, and AB = 15 ft. Find the area of the trapezoid. 30 ft2 33 ft2 44 ft2 55 ft2

Answer 1

Answer: 33 ft².

Step-by-step explanation:

1. As you can see in the figure attached, the trapezoid is formed by a rectangle and two equal right triangles. The base of each triangle is 4 feet and you know the lenght of the hypotenuse AD, therefore, you can calculate the height by applying the Pythagorean Theorem:

$h=\sqrt{(5ft)^{2}-(4ft)^{2}}=3ft$

2. Now, you can calculate the area with the following formula:

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

Where B is the longer base, b is the shorter base and h is the height.

Then:

$A=(\frac{15ft+7ft}{2})(3ft)=33ft^{2}$

Answer 2

Answer:

D. $55ft^2$

Step-by-step explanation:

The area of the trap-ezoid ABCD is given by the formula,

$Area=\frac{1}{2}(|AB|+|DC|)\times |AD|$

See diagram in the attachment.

We substitute the given values to obtain;

$Area=\frac{1}{2}(15+7)\times 5$

This simplifies to

$Area=\frac{1}{2}(22)\times 5$

This will give us;

$Area=11\times 5=55ft^2$

Therefore the correct answer is option D.