Question

problem 6
this shape is made of part of a circle and part of a square
what is the perimeter and the area of the shape?
use paper if it helps you with your thinking.
all measurements are in units.

Explanation:

Step1: Calculate the perimeter

• The perimeter of the shape consists of three sides of the large square ($10 + 10+5$), one side of the small square ($5$) and a quarter - circle arc.
• The formula for the circumference of a circle is $C = 2\pi r$. For a quarter - circle with $r = 5$, the length of the arc is $\frac{1}{4}\times2\pi r=\frac{1}{4}\times2\pi\times5=\frac{5\pi}{2}\approx\frac{5\times3.14}{2}=7.85$.
• The sum of the straight sides: $10 + 10+5 + 5=30$.
• The perimeter $P=30 + 7.85=37.85$.

Step2: Calculate the area

• The area of the large square is $A_{1}=10\times10 = 100$.
• The area of the quarter - circle is $A_{2}=\frac{1}{4}\pi r^{2}$, with $r = 5$. So $A_{2}=\frac{1}{4}\times\pi\times5^{2}=\frac{25\pi}{4}\approx\frac{25\times3.14}{4}=19.625$.
• The area of the small square (the part that is subtracted) is $A_{3}=5\times5 = 25$.
• The area of the shape $A=100-25 + 19.625=94.625$.

Answer:

Perimeter (units)	Area (sq. units)