Question

The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is 
1322 cm²

1311cm²

1392cm²

1344 cm²
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Answer 1

$\boxed{\orange{Answer=>1344\:cm²}}$

$\underline{Explanation:}$

• According to Heron's formula the area of the triangle is,

$= > \blue{\sqrt{s(s - a)(s - b)(s - c)}} \\ \\ \blue{Where, \: ‘s’(semiperimeter) } = \blue{\frac{a + b + c}{2}} \\ \blue{and, \:( a, \: b \: and \: c) \: are \: sides \: of \: triangle.}$

∴ The semiperimeter of the triangle with the sides 56 cm, 60 cm and 52 cm is,

$= >\blue{ s} = \blue{\frac{a + b + c}{2 }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =\blue{ \frac{56 + 60 + 52}{2}} \\ \\ = \blue{ \frac{168}{2}} \\ \\ \: \: \: \: \: \: = \blue{\boxed{84 \: cm}}$

∴ The area of the triangle with the sides 56 cm, 60 cm and 52 cm and semiperimeter 84 cm is,

$= >\blue{ Area} = \blue {\sqrt{s(s - a)(s - b)(s - c)}} \\ \\ = \blue{ \sqrt{84(84 - 56)(84 - 60)(84 - 52)}} \\ \\ = \blue{\sqrt{84(28)(24)(32)}} \\ \\ = \blue{ \sqrt{84 \times 28 \times 24 \times 32}} \\ \\ = \blue{\sqrt{1806336}} \\ \\ = \green{\boxed{1344 \: cm^{2} }}$

∴ The area of the triangle is 1344 cm².