How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 22 units in length?

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How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 22 units in length?

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Answer 1 · 2016-01-13T22:48:31

A ≈ 120

Explanation:

Heron's formula is a two step process :

step 1 : Calculate half of the Perimeter (s )

If the lengths of the sides are a , b and c , then

$s = \frac{a + b + c}{2}$ $s = (a + b +c )/2$

In this question let a = 15 , b = 16 and c = 22

$\Rightarrow s = \frac{15 + 16 + 22}{2} = \frac{53}{2} = 26.5$ $rArr s = ( 15 + 16 + 22 )/2 = 53/2 = 26.5$

step 2 : Calculate Area (A ) using :

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

substitute in values :

$A = \sqrt{26.5 (26.5 - 15) (26.5 - 16) (26.5 - 22)}$ $A = sqrt(26.5(26.5 - 15 )(26.5 -16 )(26.5 - 22 )$

$\Rightarrow A = \sqrt{26.5 \times 11.5 \times 10.5 \times 4.5} = \sqrt{14399.4375} \approx 120$ $rArr A = sqrt(26.5 xx 11.5 xx 10.5 xx 4.5 ) = sqrt14399.4375 ≈ 120$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 22 units in length?

1 Answer

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