Question

Calculate the shaded area...​

Answer 1

Hey Mate!!

Given ;

Sides of triangle = 16 cm and 12 cm

By Pythagoras theorem ;

12^2 + 16^2 = x^2

144+256 = x^2

√400 = x

x = 20 cm.

So the other side is 20 cm which is the diameter of semi circle.

So, area of semi circle = πr^2 /2

22/7 × 10×10 /2 [ d/2 = r ; 20/2 = 10 ]

Area of semi circle = 157.142 cm^2

By using Heron's formula, we can calculate the area of the triangle.

Heron's formula ; A = √ s ( s-a) (s-b) s-c)

"S" here is semi - Perimeter

Perimeter = 12+16+20 = 48 cm

semi - perimeter = 48/2 = 24 cm

√ s (s-a) (s-b) (s-c)

√ 24 (24-12) (24-16) (24-20)

√ 24 (12) (8) (4)

√9216 = 96 cm^2

Therefore ;

Area of shaded region = Area of semi circle - area of triangle

Area of shaded region =

157.142 cm^2 - 96 cm^2

Area of shaded region = 61.142 cm^2

Hope this helps you!!

Answer 2

Answer:

61cm^2

Step-by-step explanation:

Hi mate!!!

(refer attachment for diagram)

Area of Triangle ABC = $\text \frac {1}{2} L*B$

Area of Triangle ABC = $\text \frac {1}{2} 16*12$

Area of Triangle ABC = 96cm^2 ----------(1)

AC = $\sqrt {AB^2 + BC^2}$

AC = $\sqrt {16^2 + 12^2}$

AC = $\sqrt {400}$

AC = 20cm.

Area of semi circle = (π*r^2)/2

r = 20/2 = 10cm.

Area of semi circle = (π*10*10)/2

Area of semi circle = 3.14 *100/2

Area of semi circle = 157cm^2-----------(2)

Area of shaded region = Area of semi circle - Area of Triangle ABC

Area of shaded region = (157 - 96)cm^2 [from (1) & (2)]

Area of shaded region = 61cm^2.

HOPE IT HELPS!!!

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