Question

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

Answer 1

`Area = 26478cm^2`

Explanation:

Given

See attachment for desk

Required

The area

First, calculate the area of the semicircular cutout

`Area = (\pi r^2)/(2)`

Where

`r = 60cm`

So:

`A_1 = (3.14 * 60^2)/(2)`

`A_1 = (11304)/(2)`

`A_1 = 5652cm^2`

Next, the area of the complete trapezium

`Area= (1)/(2)(a + b) * h`

Where

`a = 300`

`b = 2 * r = 2 * 60 = 120`

`h = 153`

So:

`A_2 = (1)/(2) * (300 + 120) * 153`

`A_2 = (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`