Question

Find the perimeter of the shaded region (Shaded region is in blue) .AB+AD=10cm

Answer 1

Answer:

area of shaded region = area of quadrant - area of right angles triangle. use this formula

Answer 2

Answer:

41.27 cm²

Step-by-step explanation:

Find the area of the quadrant:

Area of the quadrant = 1/4 πr²

Area of the quadrant = 1/4 π(8)²

Area = 16π cm²

Find the area of the triangle:

Area = 1/2 x base x height

Area = 1/2 x AD x AB

Area = 1/2 (AD)(AB)

We can deduce that:

BD = AC = radius = 8 cm

Also,

ABD is a right angle triangle

AD² + AB² = BD²

AD² + AB² = 8²

(AD + AB)² - 2(AD)(AB) = 64

10² - 2(AD)(AB) = 64

2(AD)(AB)  = 100 - 64

2(AD)(AB)  = 36

(AD)(AB) = 18 cm

Now find the area of the triangle:

Area = 1/2 (AD)(AB)

Area = 1/2 (18)

Area = 9 cm²

Find the area of the shaded region:

Area of the shaded region = Area of the quadrant - Area of the triangle

Area of the shaded region = 16π - 9

Area of the shaded region = 41.27 cm²

Answer: 41.27 cm²