Mathematics: PLEASE I NEED HELP WITH MY MATHS HOMEWORK I HAVE SO MUCH HOMEWORK DURING THIS QUARANTINE USE THE IMAGE ATTACHED BELOW TO HELP ME The diagram shows a square ABCD with sides of length 20cm It also shows a semicircle and arc of a circle. AB is the diameter of the semicircle BD is an arc of a circle with centre A a) Find the area of the shaded region giving your answer in terms of π You must show your working,clearly stating the area of the semicircle

14: increase 15: decreaseHope this helps!...

PLEASE I NEED HELP WITH MY MATHS HOMEWORK I HAVE

Ответ:

angelteddy033

23.01.2022

Mathematics

a) The area of the shaded region is 50π.

b) $\frac{Area of the shaded region}{area of square} = \frac{\pi}{8} .$

Step-by-step explanation:

Step 1:

The area of a circle $= \pi r^{2}.$

The area of a semi-circle $= \frac{\pi r^{2} }{2} .$

The area of a quarter-circle $= \frac{\pi r^{2} }{4} .$

The shaded region's area is obtained by subtracting the area of the semi-circle with a radius of 10 cm from the area of a quarter-circle with a radius of 20 cm.

The area of the semi-circle with a radius of 10 cm $= \frac{\pi (10^{2}) }{2} .$

The area of the quarter-circle with a radius of 20 cm $= \frac{\pi (20^{2}) }{4} .$

Step 2:

The area of the shaded region is obtained by subtracting these areas.

The area of the shaded region $= \frac{\pi (20^{2}) }{4} - \frac{\pi (10^{2}) }{2} .$

$\frac{\pi (20^{2}) }{4} - \frac{\pi (10^{2}) }{2} = \frac{\pi}{2} (\frac{20^{2} }{2} -10^{2} ).$

$\frac{\pi}{2} (\frac{20^{2} }{2} -10^{2} ) = \frac{\pi}{2} (\frac{400}{2} -100 ) = \frac{\pi}{2} (100).$

$\frac{\pi}{2} (100) = 50 \pi.$

The area of the shaded region is 50π square units.

Step 3:

The area of a square is the square of the side length.

The area of the square $= 20^{2} = 400$ square cm.

b) $\frac{Area of the shaded region}{area of square} =\frac{50\pi}{400} =\frac{\pi}{8} .$

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