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

D.
`55ft^2`

Explanation:

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

`Area=(1)/(2)(|AB|+|DC|)* |AD|`

See diagram in the attachment.

We substitute the given values to obtain;

`Area=(1)/(2)(15+7)* 5`

This simplifies to

`Area=(1)/(2)(22)* 5`

This will give us;

`Area=11* 5=55ft^2`

Therefore the correct answer is option D.

Answer 2

Answer: 33 ft².

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=((B+b)/(2))h`

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

Then:

`A=((15ft+7ft)/(2))(3ft)=33ft^(2)`