Math, asked by nehalchopra2006, 16 days ago

calculate the area of the shaded region in☝️​
(its urgent)(use herons formula)​

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Answers

Answered by bangtangranger
13

Answer:

1074 m²

Step-by-step explanation:

First we need to find the area of the larger triangle.

Given, sides of larger triangle(a, b, c) are 120 m, 122 m, 22 m

Semi-perimeter = (120+122+22)/2

                          = 264/2

                          = 132 m//

According to Heron's Formula: \sqrt{s(s-a)(s-b)(s-c)}

\sqrt{132(132-120)(132-122)(132-22)} \\= \sqrt{132(12)(10)(110)} \\= \sqrt{(3*2*2*11)(3*2*2)(2*5)(11*2*5)}\\(pair the like numbers and take out of square root)

= 3 x 2 x 11 x 2 x 2 x 5

= 1320 m²//

Now we need to find the area of the smaller triangle

Given, sides of the smaller triangle (a, b, c) are 26 m, 24 m, 22 m

Semi-perimeter = (26+24+22)/2

                          = 72/2

                          = 36 m//

Apply heron's formula and find area

\sqrt{36(36-26)(36-24)(36-22)}\\= \sqrt{36(10)(12)(14)}\\=\sqrt{(6*6)(2*5)(2*3*2)(2*7)}\\= 24\sqrt{105\\

Area of shaded figure = area of larger triangle - area of smaller triangle

= 1320 - 24√105

approx. value of √105 = 10.25

area = 1320 - 24(10.25)

        = 1074 m²//

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