Question

O4
6. find the area of triangle whose sides are
8 m, 5 m, 7 m.
1 D.​

Answer 1

answer:

by using herons formula

s=8+5+7/2

=20/2

=10

area= whole root s(s-a)(s-b)(s-c)

= root 10(2)(5)(3)

=10 root 3(answer)

Answer 2

Given:-

• Sides of triangle are 8 m , 5 m and 7 m.

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To find:-

• Area of triangle.

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$\huge\bf\underline\red{\:Solution}$

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Height is not given. So, we do not use $\large \tt \frac{1}{2}$ × base × height.

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We use Heron's formula in this case. So formula of Heron's formula is :-

$\large \tt \sqrt{s(s - a)(s - b)(s - c)}$

In which

• S is semi-perimeter of triangle.
• a , b and c are sides of triangle.

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So,

Semi-perimeter = $\large \tt \frac{Perimeter\:of\: triangle}{2}$

• Perimeter of triangle is sum of all sides.

$\implies \large \tt \frac{8 + 5 + 7}{2}$

$\implies \large \tt \frac{20}{2}$

$\implies \large \tt 10$

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☄ Semi-perimeter is 10 cm.

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Area of triangle

$\implies \tt \sqrt{10(10 - 8)(10 - 5)(10 - 7)}$

$\implies \tt \sqrt{10 \times 2 \times 5 \times 3}$

• Factors of 10 are 2 and 5.

$\implies \tt \sqrt{2 \times 5 \times 2 \times 5 \times 3}$

$\implies \tt \:2 \times 5 \sqrt{3}$

$\implies \tt\: 10\: \sqrt{3}$

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☀Thus, Area of triangle is 10√3 cm².