Question

A pinwheel's four blades are all congruent right trapezoids.

4 in

2 in

2 in

What is the combined area of the four blades, in square inches?

Answer 1

`Area = 24\ in^2`

Explanation:

Given

Let

`a, b \to` opposite sides of each trapezoid

`h \to` height

`a = 2; \ \ \ b = 4 \ \ \ \ h = 2`

See attachment for trapezoids

Required

The combined area of the 4

First, we calculate the area of 1

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

So:

`A_1 = (1)/(2)(2 + 4) * 2`

`A_1 = (1)/(2)*6 * 2`

Using a calculator

`A_1 = 6`

The combined area is:

`Area =n * A_1`

Where

`n = 4` --- 4 blades

So:

`Area = 4 * 6`

`Area = 24\ in^2`