Question

The diagram shows part of a fan. OFG and OAD are sectors, centre 0, with radius 18 cm and sector angle 40° B, C, H and E lie on a circle, centre O and radius 6 cm. Calculate the shaded area.​

Answer 1

The area of a shape is the amount of space on it:

The shaded area is 314 square centimeters

How to determine the shaded area

Start by calculating the area of sectors OFG and OAD using:

$A = \frac{\theta}{360} * \pi r^2$

So, we have:

$OFG = \frac{40}{360} * \pi * 18^2$

$OFG = 36\pi$

Also, we have:

$OAD = \frac{40}{360} * \pi * 18^2$

$OAD = 36\pi$

Next, calculate the area of the sectors BOE and COH

Note that the radius of these sectors is 6 cm.

So, we have:

$COH =BOE = \frac{140}{360} * \pi * 6^2$

$COH = BOE = 14\pi$

The shaded area is then calculated as:

$Shaded = OFG + OAD + COH + BOE$

This gives

$Shaded =36\pi + 36\pi + 14\pi + 14\pi$

$Shaded =100\pi$

The equation becomes

$Shaded =100 * 3.14$

$Shaded = 314$

Hence, the shaded area is 314 square centimeters

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