Question

The sides of a triangle are 16 cm, 30 cm and 34 cm respectively. At each vertices, circles of radius 7 cm are drawn. What is the area of the triangle. Excluding the portion covered by the sectors of the triangle?

Answer 1

Step-by-step explanation:

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Answer 2

1) Let the angles of the triangle be x, y, z, so x+y+z =180

2) Since x, y, z are also the the angles of sectors. Hence, the total area covered by the sectors would be equal to area covered by an semicircle of radius 7.

3) Area of triangle by Heron's Formula :

$\sqrt{s(s-a)(s-b)(s-c)}$ where s = (a + b+ c)/2

4) s = (16+30+34)/2 = 40 cm.

Area = $\sqrt{40(40-16)(40-30)(40-34)}$ = $\sqrt{40*24*10*6}$ =  240 square cm.

5) Area of semicircle = $(\pi r^2)/2$ = (22/7*7*7)/2 = 77 square cm.

6) Hence the area of the triangle. Excluding the portion covered by the sectors of the triangle would be 240 - 77 = 163 square cm