How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 7, and 13 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 14, 7, and 13 units in length?

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Answer 1 · 2016-02-05T16:56:40

Area ≈ 45.17

Explanation:

Calculating the area is a 2 step process.

step 1 : calculate ( half the perimeter of the triangle = s )

step 2 : calculate the area using

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

let a = 14 , b = 7 and c = 13

step 1 : $s = \frac{a + b + c}{2} = \frac{14 + 7 + 13}{2} = \frac{34}{2} = 17$ $s = (a+b+c)/2 = (14+7+13)/2 = 34/2 = 17$

step 2 : $A = \sqrt{17 (17 - 14) (17 - 7) (17 - 13)}$ $A = sqrt(17(17-14)(17-7)(17-13))$

$= \sqrt{17 \times 3 \times 10 \times 4} \approx 45.17 square units$ $= sqrt(17 xx 3 xx 10 xx 4) ≈ 45.17color(black)(" square units" )$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 7, and 13 units in length?

1 Answer

Explanation:

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