What is the area of the trapezoid? Leave the answer in simplest radical form.

Question

asked Jul 23, 2020 231k views

2 Answers

Median Hilal · Answer 1 · 2020-07-30T09:14:40+0000

For this case we must find the area of the figure composed of a triangle and a rectangle.

Triangle area:

$A_ {t} = \frac {b * h} {2}$

Where b is the base and h is the height.

Area of the rectangle:

$A_ {r} = a * b$

Where a and b are the sides.

The base of the triangle measures:

13-5 = 8

We find the height by trigonometry:

$tg (45) = \frac {h} {b}\\1 = \frac {h} {b}\\b = h$

So:

$A_ {t} = \frac {8 * 8} {2}\\A_ {t} = 32 \ ft ^ 2$

On the other hand:

$A_ {r} = 5 * 8\\A_ {r} = 40 \ ft ^ 2$

Thus, the total are the sum:

$(32 + 40) ft ^ 2 = 72 \ ft ^ 2$

Answer:

Option A