Expert answers to "In the figure 2 semicircles, each of diameter..."

High School
Geometry
High school geometry
Solid Geometry

banganX

Answered question

2021-05-21

In the figure 2 semicircles, each of diameter 28m, are removed from the rectangle. Find
(i) the perimeter,
(ii) the are,
of the shaded region.

Answer & Explanation

Roosevelt Houghton

Skilled2021-05-22Added 106 answers

(i)The perimeter is sum of the two lengths and the two half-circumferences, with radius $28 / 2 = 14 c m$ :
$P = 40 + 40 + (\frac{1}{2}) [2 π (14)] + (\frac{1}{2}) [2 π (14)]$
$P = 80 + 14 π + 14 π$
$P = 80 + 28 π \sim 167.96 c m$
(ii)The area is the area of the rectangle minus the areas of the two semicircles: $A = (40) (28) - (\frac{1}{2}) (π \cdot 14^{2}) - (\frac{1}{2}) (π \cdot 14^{2})$
$A = 1120 - 98 π - 98 π$
$A = 1120 - 196 π \sim 504.25 c m^{2}$

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