Question

Find the area of the shaded region.6005 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.

Answer 1

To determine the area of the shaded region we first need to calculate the area of the whole circle, then we need to calculate the area of the circular sector of 60º, then finally we will calculate the area of the triangle and subtract the area of the triangle from the area of the circular sector, this will be the area of the part that isn't painted. Finally we can subtract the area that isn't painted by the area of the circle to determine the shaded region.

To calculate the area of the circle we will do as follows:

`A_{\text{circle}}=\pi\cdot r^2=\pi\cdot5^2=25\cdot\pi=78.5`

The circular sector can be calculated by the following expression:

`A_{\text{sector}}=(60\cdot\pi\cdot r^2)/(360)=(\pi\cdot5^2)/(6)=(25\cdot\pi)/(6)=13.08`

All of the sides of the triangle are equal, so we can use the following expression:

`A_{\text{triangle}}=\frac{l^2\sqrt[]{3}}{4}=\frac{5\cdot\sqrt[]{3}}{4}=2.163`

Now we will subtract the area of the triangle from the area of the sector to determine the area that isn't shaded.

`A_{\text{blank}}=13.1-2.163=10.937`

To finish we will subtract the area that isn't shaded from the area of the circle.

`A_{\text{shaded}}=78.54-10.937=67.6`

The area of the shaded region is 67.6 cm²