How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 18, and 19 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, 18, and 19 units in length?

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Answer 1 · 2016-03-26T12:14:18

Area $= 126.554$ $=126.554" "$ square units

Explanation:

Let the sides be $a = 15$ $a=15$ and $b = 18$ $b=18$ and $c = 19$ $c=19$

Solve for the half perimeter $s = \frac{a + b + c}{2} = \frac{15 + 18 + 19}{2} = 26$ $s=(a+b+c)/2=(15+18+19)/2=26$

The Heron's Formula for the area of the triangle

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

Area $= \sqrt{26 (26 - 15) (26 - 18) (26 - 19)}$ $=sqrt(26(26-15)(26-18)(26-19))$

Area $= 126.554$ $=126.554" "$ square units

God bless....I hope the explanation is useful.

Answer 2 · 2016-03-26T12:21:14

≈ 126.55 square units

Explanation:

This is a 2 step process.

step 1 : Calculate half the perimeter (s) of the triangle.

let a = 15 , b = 18 and c = 19

$s = \frac{a + b + c}{2} = \frac{15 + 18 + 19}{2} = \frac{52}{2} = 26$ $s = (a+b+c)/2 = (15+18+19)/2 = 52/2 = 26$

step 2 : Calculate the area using

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

$= \sqrt{26 (26 - 15) (26 - 18) (26 - 19)}$ $= sqrt(26(26-15)(26-18)(26-19))$

$= \sqrt{26 \times 11 \times 8 \times 7} \approx 126.55 square units$ $= sqrt(26xx11xx8xx7) ≈ 126.55" square units "$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 18, and 19 units in length?

2 Answers

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