Question

Heron’s formula: Area 

Answer 1

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Answer 2

Triangle is attached below

The triangle is 12 by 10 by 8

Perimeter:

To find perimeter we add all the sides of the triangle

Perimeter P = 12 + 10 + 8 = 30 units

Semi perimeter:

Semi perimeter is half of its perimeter

We know P = 30

Semi perimeter s= $\frac{p}{2}$ = $\frac{30}{2}$ = 15 units

Area:

If we know the sides of the triangle then we use Heron's formula to find the area of the triangle

$A = \sqrt{s(s-a)(s-b)(s-c)}$

Where s= semi perimeter

a,b,c are the sides of the triangle

s= 15 units

a= 12 units

b= 10 units

c= 8 units

$A = \sqrt{15(15-12)(15-10)(15-8)}$

$A= \sqrt{15(3)(5)(7)}$

$A= \sqrt{15 * 105}$

$A= \sqrt{1575}$

A= 39.7 square units