Question

Calculate the area of each of these shapes

Answer 1

Answer:

a)  Semicircle's area

• $\frac{1}{2} (\pi . radius^{2} )$
• = $\frac{1}{2}$ x $\frac{22}{7}$ x 8 x 8
• = $\frac{704}{7}$
• = 100. 571 sq.cm

b) 1/4th of circle or quadrant

•  $\frac{\pi r^{2} }{4}$
• = $\frac{1}{4}$ x $\frac{22}{7}$ x 10 x 10
• = $\frac{550}{7}$
• = 78 .571 sq.cm

c) A part of a circle

• 360/30 = 12
• Area = $\frac{\pi r^{2} }{12}$
• = $\frac{22 X 15 X 15}{12 X 7}$
• = $\frac{4950}{84}$
• = 58.928 sq.cm

d) Area of figure =  Semicircle + Rectangle

• ( $\frac{6 X 6 X 22}{2 X 7}$ )+ ( 8 x 6)
• = 56.571 + 48
• = 104.571 sq.cm

e) Area of three-sided concave figure

• Suppose the hypotenuse is  part of circle A and figure part of square B
• Circle A of radius r contains 90° arc (hypotenuse)
• Due to tangency, the other two sides form a right angle/
• The area of the figure is the difference between the area of square B and the circular sector of circle A.
• The area of a square B = $3^{2}$ = 9 sq.cm
• The area of the sector is  90°/360°  (or 1/4) of the area of circle A, yielding  πr2/4 = $\frac{22x3x3}{7x4}$ = 7.01
• Area = 9 - 7.01 = 1.98 sq.cm

f) Area of the figure

• Circle + 2 semicircles or 1 smaller circle
• = $\frac{22X3X3}{7}$ + $\frac{22 X 1 X 1}{7}$
• =  28.28 + 3.14
• = 31.42 sq.cm