A child makes a poster on a chart paper drawing a square ABCD of side 14cm. She draws four circles with centre A,B,C and D in which she suggests different ways to save energy. The circles are drawn in such away that each circle touches externally two of the three remaining circles (Fig.15.74). In the shaded region she writes a message ‘Save Energy’. Find the perimeter and area of the shaded region.(Use π=22/7)
Answers
The perimeter and area of the shaded region are 44m and 42m²
respectively.
•Since , the circles are of same
radius
• let the radius of circle is r
• now, AB = 14m
• AE + EB = 14
• r + r = 14
• 2r = 14
• r = 7m
• area covered by circular part =
1/4 (πr²)
• area covered by 4 cicular parts =
(πr²)
• area = 22*7*7/7
• Area = 154 m²
• Area of square = 14*14 = 196m²
• shaded area = 196-154 = 42m²
• similarly ,
perimeter of circular part = 1/4 (2πr) •Perimeter of 4 cicular parts = 2πr
• Perimeter of shaded region = 2πr
= 2*22*7/7
=44m
Area of shaded region = 42 cm² , Perimeter of Shaded region = 44 cm
Step-by-step explanation:
Square ABCD of side 14cm.
=> Radius of Each circle = 14/2 = 7 cm
Area of Square ABCD = 14 * 14 = 196 cm²
Area of circle in square = 4 * (90°/360°) π (7)²
= (22/7) * 7²
= 154 cm²
area of shaded region = 196 - 154 = 42 cm²
Perimeter of Shaded region = 4 *(90°/360°) 2 π * 7
= 2 * (22/7) * 7
= 44 cm
Perimeter of Shaded region = 44 cm
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