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

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:

[tex]h=\sqrt{(5ft)^{2}-(4ft)^{2}}=3ft[/tex]

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

[tex]A=(\frac{B+b}{2})h[/tex]

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

Then:

[tex]A=(\frac{15ft+7ft}{2})(3ft)=33ft^{2}[/tex]

kudzordzifrancis kudzordzifrancis · Answer 2 · 2019-01-22T01:43:40+01:00

kudzordzifrancis kudzordzifrancis

22-01-2019

Answer:

D. [tex]55ft^2[/tex]

Step-by-step explanation:

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

[tex]Area=\frac{1}{2}(|AB|+|DC|)\times |AD|[/tex]

See diagram in the attachment.

We substitute the given values to obtain;

[tex]Area=\frac{1}{2}(15+7)\times 5[/tex]

This simplifies to

[tex]Area=\frac{1}{2}(22)\times 5[/tex]

This will give us;

[tex]Area=11\times 5=55ft^2[/tex]

Therefore the correct answer is option D.

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