Question

The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

• The area of the figure will be 5π/2 in².
• The perimeter will be 3π + 2 in

Step-by-step explanation:

This figure is a combination of two semi-circles.

• One having diameter of 2 inches i.e. AD
• Other having diameter of 4 inches i.e. AC

As

${\displaystyle \pi ={\frac {C}{d}}}$

${{{C}}}=\displaystyle \pi.d$

Perimeter of the big figure could be computed by cutting the perimeters of each circle in half, and then combing them together.

Area could be computed using the same way.

Calculating the Perimeter:

• As the circumference of the smaller circle is 2π in. Cutting it half would yield the circumference of the smaller semi-circle i.e. π.

• As the circumference of the bigger circle is 4π in. Cutting it half would yield the circumference of the bigger semi-circle i.e. 2π.

• As the length of the segment DC is 2 in.

So, the total perimeter would be: π + 2π + 2 = 3π + 2 in

Calculating the Area

Area could be computed using the same way as we did during measuring perimeter.

As the area of circle is

$A={\displaystyle \pi.r^{2}$

As we are dealing with semi-circles. So, cutting the diameters of two semi-circles in half can let us find the radii of them.

So,

• Smaller semi-circle has 1 in radius
• Larger semi-circle has 2 in radius

Areas would have to be cut in half as well, as we are dealing with semi-circles.

So,

For smaller:

$A_{small} =\frac{1}{2} {\displaystyle \pi.r^{2}$

$A_{small} =\frac{1}{2} {\displaystyle \pi.(1)^{2}$

$A_{small} =\frac{1}{2} {\displaystyle \pi$

Hence, the area of smaller will be: π/2 in²

For larger:

$A_{larger} =\frac{1}{2} {\displaystyle \pi.r^{2}$

$A_{larger} =\frac{1}{2} {\displaystyle \pi.(2)^{2}$

$A_{larger} =2 \pi^{}$

Hence, the area of larger will be: 2π in²

Combining them together:

$\frac{1}{2} {\displaystyle \pi^{} + 2 {\displaystyle \pi^{}=\frac{5}{2} {\displaystyle \pi^{}$

Therefore,

• The area of the figure will be 5π/2 in².
• The perimeter will be 3π + 2 in

Keywords: radius, area, perimeter, semi-circle, circle, diameter, circumference of circle

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