In the given figure AB AE EF FG and GB are

In the given figure, AB, AE, EF, FG and GB are semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in cm²) of the shaded region?
Mensuration 2D mcq question image

A. 414.46

B. 382.82

C. 406.48

D. 394.24

Answer: Option D

Solution (By Examveda Team)

AB = 56 cm
AE = EF = FG = GB = 14 cm
∴ EM = MF = 7 cm
PF = $$\frac{{56}}{2}$$ = 28 cm
OF = 28 - r
OM = 7 + r
MF = 7
In ΔOMF,
OM² = OF² + MF²
(7 + r)² = (28 - r)² + 7²
49 + r² + 14r = 784 + r² - 56r + 49
70r = 784
r = $$\frac{{784}}{{70}}$$ = 11.2
Area of circle = πr²
= $$\frac{{22}}{7} \times \frac{{112}}{{10}} \times \frac{{112}}{{10}}$$
= 394.24 cm²

If the given figure, in a right angle triangle ABC, AB = 12 cm and AC = 15 cm. A square is inscribed in the triangle. One of the vertices of square coincides with the vertex of triangle. What is the maximum possible area (in cm²) of the square?

A. $$\frac{{1296}}{{49}}$$

B. $$25$$

C. $$\frac{{1225}}{{36}}$$

D. $$\frac{{1225}}{{64}}$$

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In the given figure, AB, AE, EF, FG and GB are semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in cm²) of the shaded region?

Solution (By Examveda Team)

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