How do you use Heron's formula to determine the area of a triangle with sides of that are 28, 29, and 32 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 28, 29, and 32 units in length?

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Answer 1 · 2016-05-02T09:27:27

Area of triangle is $377.175$ $377.175$ units

Explanation:

If the three sides of a triangle are $a$ $a$ , $b$ $b$ and $c$ $c$ , according to Heron's formula, area of triangle is given by

$\sqrt{s (s - a) (s - b) (s - c)}$ $sqrt(s(s-a)(s-b)(s-c))$ where $s = \frac{1}{2} (a + b + c)$ $s=1/2(a+b+c)$

Here the three sides are $28$ $28$ , $29$ $29$ and $32$ $32$ and hence

$s = \frac{1}{2} (28 + 29 + 32) = \frac{89}{2}$ $s=1/2(28+29+32)=89/2$

Hence area of triangle is

$\sqrt{\frac{89}{2} \times (\frac{89}{2} - 28) \times (\frac{89}{2} - 29) \times (\frac{89}{2} - 32)}$ $sqrt(89/2xx(89/2-28)xx(89/2-29)xx(89/2-32)$

or = $\sqrt{\frac{89}{2} \times \frac{33}{2} \times \frac{31}{2} \times \frac{25}{2}}$ $sqrt(89/2xx33/2xx31/2xx25/2)$

or $\frac{5}{4} \sqrt{89 \times 33 \times 31} = \frac{5}{4} \sqrt{91047} = \frac{5}{4} \times 301.74 = 377.175$ $5/4sqrt(89xx33xx31)=5/4sqrt91047=5/4xx301.74=377.175$ units.

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How do you use Heron's formula to determine the area of a triangle with sides of that are 28, 29, and 32 units in length?

1 Answer

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