Question

find the area of the triangle whose measures three sides are 36 cm, 56 cm, 36 cm.

Answer 1

$using \: herons \: formula \sqrt{s(s - a)(s - b)(s - c)} \\ where \: s \: is \: semiperimeter,a ,b, c are sides$
semiperimeter=(36+36+56)÷2=64
so area
$\sqrt{64 \times (64 - 36)(64 - 56)(64 - 36)} \\ = \sqrt{64 \times 28 \times 8 \times 28} \\ = 633.56$
so area =633.56cm2

Answer 2

Answer :


Given sides of triangle are -

36cm,56cm and 36cm


When sides of a triangle are given then we can find it's area by using Heron's formula.

Which is --


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

Here s refers to semi-perimeter

and a,b and c are the sides of triangle.

Let a = 36cm

b = 56cm

c = 36cm

$semiperimeter \: (s) = \frac{a + b + c}{2} \\ \\ s = \frac{36 + 56 + 36}{2} \\ \\ s = \frac{128}{2} \\ \\ s = 64cm$

$now \: area \: of \: triangle \: = \\ \\ \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sqrt{64(64 - 36)(64 - 56)(64 - 36)} \\ \\ \sqrt{64 \times 28 \times 8 \times 28} \\ \\ \sqrt{401408} \\ \\ 448\sqrt{2} \\ \\ 633.56 \: cm {}^{2}$


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