Question

2.If the sides of a triangle are 20cm,24cm and 28cm,find its area *

Answer 1

$\bf \underline{GIVEN:- } \: \sf{Sides \: of \: triangles \: are \: 20,24 \: and \: 28cm}.$

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$\bf \underline{TO \: FIND:-} \: \sf{Area \: of \: triangle.}$

$\bf \underline{SOLUTION:-}$

$\sf \: Herons \: formula = \sqrt{s(s - a)(s - b)(s - c)}$

By using Heron's Formula,

$\sf \: S = \dfrac{Sum \: of \: side}{2}$

$\sf S = \dfrac{20 + 24 + 28}{2}$

$\sf \: S = 36cm$

Now,

$\sf \: Area \: of \: triangle = \sqrt{36(36 - 20)(36 - 24)(36 - 28)}$

$\sf \: \: \: \: = \sqrt{36 (16)(12)(8)}$

$\sf \: \: \: \: = \sqrt{36 \times 1536}$

$\sf \: \: \: \: = \sqrt{55296}$

$\sf \: \: \: \: = 235.1cm {}^{2}$

Therefore, area of triangle is 235.1cm².

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Heron's formula calculate the area of a triangle with given length of each side. If the length of 3 sides is known, then we can find the area of a triangle through Heron's Formula.

If we're having base and height of triangle, then we can use: 1/2×base×height identity to find its area.

Answer 2

Given ,

• The measures of sides of triangle are 20 cm , 24 cm and 28 cm

We know that ,

The semi perimeter of triangle is given by

Semi perimeter (s) = (a + b + c)/2

Thus ,

s = (20 + 24 + 28)/2

s = 72/2

s = 36 cm

Now , the area of triangle is given by

$\boxed{ \sf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}$

Thus ,

Area = √{36(36-20)(36-24)(36-28)}

Area = √{36 × 16 × 12 × 8}

Area = √36 × √16 × √96

Area = 6 × 4 × 2.44

Area = 96 × 2.44

Area = 234.4 cm² (approx)

Therefore ,

• Thee area of triangle is 234 cm²