Question

Jillian is making a paper flower motif for an art project the flower she is making has 4 petals each petal is made of three semicircles as shown below, What is the area of the paper flower?

Answer 1

`Area = 216\pi`

Explanation:

Given

See attachment for semicircles

Required

The area of the paper

First, calculate the area of each petal.

The petal is made up of:

1. Semicircle of diameter 12cm

2. Semicircle of diameter 18cm (i.e. 12cm + 6cm)

3. A hole semicircle of diameter 6cm

The area of each semicircle is calculated as follows:

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

For (1):

`d = 12cm` --- diameter

`r = 0.5 * d = 0.5* 12cm = 6cm` --- radius

So:

`A_1 = (\pi * 6^2)/(2)`

Evaluate the exponent

`A_1 = (\pi * 36)/(2)`

Divide 36 by 2

`A_1 = 18\pi`

For (2):

`d = 18cm`

`r = 0.5* 18cm = 9cm`

So:

`A_2 = (\pi * 9^2)/(2)`

`A_2 = (\pi * 81)/(2)`

`A_2 = 40.5\pi`

For (3):

`d = 6cm`

`r = 0.5* 6cm = 3cm`

So:

`A_3 = (\pi * 3^2)/(2)`

`A_3 = (\pi * 9)/(2)`

`A_3 = 4.5\pi`

Recall that (3) is a hole.

So, the area (A) of a petal is:

`A = A_1 + A_2 - A_3`

`A = 18\pi + 40.5\pi - 4.5\pi`

`A = 54\pi`

The paper uses 4 petals.

So:

`Area = 4 * A`

`Area = 4 * 54\pi`

`Area = 216\pi`