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

AREA:

so you have 2 halves, and 1 quarter, of a circle

that is 1 1/4 of a circle

the radius is 5, so we can calculate the area like this:

5^2*pi*1.25

25*1.25*pi

31.25pi

PERIMETER:

same deal as with area:

2pi*5*1.25+5+5

the two 5s that we add are the two flat parts in the diagram

12.5pi+10

FORMULAS:

pi*radius^2 for area

2pi*radius for perimeter

hope this helps!

Answer 2

This figure represents a circle and a quarter circle with a radius of length 5 cm. The area of the circle is π
`*r^(2)`. In our problem we will multiply the area of a circle by 1.25 (as we have a circle and a quarter).

`Area of a circle= pi* r^2 = 3.14*5^2=98.125 cm^2`

`Total area= Area of a circle* 1.25`

while the perimeter is
`2*pi*r`.

`Perimeter of a circle (P1)= 2*pi*r=2*5*3.14=31.4 cm`

`Perimeter of a 1/4 circle(P2)= 2*pi*r/4 +r+r=17.85 cm`

`The total perimeter = P1+P2 =49.25 cm`