Question

If square is a square of side 10cm then find the area of the shaded region

Answer 1

Answer:

Area of shaded region = 57 sq cm

Step-by-step explanation:

area of quadrant PQRT - area of triangle PQR we get area of shape PTR

area of quadrant PQRT =

$\frac{x}{360} \times \pi {r}^{2} \\ = \frac{90}{360} \times \frac{22}{7} \times 10 \times 10 \\ = \frac{22 \times 100}{4 \times 7} \\ = \frac{22 \times 25}{7} \\ =78.5 \\ area \: of \: triangle \: pqr \: = \frac{1}{2} \times 10 \times 10 \\ = 5 \times 10 = 50$

area of shape PTR = 78.5 - 50 = 28.5 (1)

$\frac{x}{360} \times \pi {r}^{2} \\ = \frac{90}{360} \times \frac{22}{7} \times 10 \times 10 \\ = \frac{22 \times 100}{4 \times 7} \\ = \frac{22 \times 25}{7} \\ =78.5 \\ area \: of \: triangle \: psr \: = \frac{1}{2} \times 10 \times 10 \\ = 5 \times 10 = 50$

area of shape PCR =

area of quadrant PCRS - area of triangle PSR

= 78.5 - 50 = 28.5 (2)

Area of shaded region PCRT = (1) + (2)

28.5 + 28.5 = 57 sq cm