Question

A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk?

Answer 1

Answer:

$Area = 26478cm^2$

Step-by-step explanation:

Given

See attachment for desk

Required

The area

First, calculate the area of the semicircular cutout

$Area = \frac{\pi r^2}{2}$

Where

$r = 60cm$

So:

$A_1 = \frac{3.14 * 60^2}{2}$

$A_1 = \frac{11304}{2}$

$A_1 = 5652cm^2$

Next, the area of the complete trapezium

$Area= \frac{1}{2}(a + b) * h$

Where

$a = 300$

$b = 2 * r = 2 * 60 = 120$

$h = 153$

So:

$A_2 = \frac{1}{2} * (300 + 120) * 153$

$A_2 = \frac{1}{2} * 420 * 153$

$A_2 = 32130cm^2$

The area of the desk is:

$Area = A_2 - A_1$

$Area = 32130cm^2 - 5652cm^2$

$Area = 26478cm^2$