A triangle has sides with lengths: 4, 5, and 7. How do you find the area of the triangle using Heron's formula?

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A triangle has sides with lengths: 4, 5, and 7. How do you find the area of the triangle using Heron's formula?

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Answer 1 · 2016-02-17T13:31:27

$4 \sqrt{6} \approx 9.8 square units$ $4sqrt6 ≈ 9.8 " square units "$

Explanation:

This is a 2 step process.

step 1 : Calculate half of the perimeter ( s ) of the triangle.
step 2 : Calculate the area (A)

let a = 4 , b = 5 and c = 7

step 1 : s = $\frac{a + b + c}{2} = \frac{4 + 5 + 7}{2} = \frac{16}{2} = 8$ $(a + b + c )/2 = (4 + 5 + 7)/2 = 16/2 = 8$

step 2 : $A = \sqrt{s (s - a) (s - b) (s - c)}$ $A = sqrt(s(s-a)(s-b)(s-c) )$

$= \sqrt{8 (8 - 4) (8 - 5) (8 - 7)} = \sqrt{8 \times 4 \times 3 \times 1} = \sqrt{96} = 4 \sqrt{6}$ $= sqrt(8(8-4)(8-5)(8-7)) = sqrt(8 xx 4 xx 3 xx 1) =sqrt96 = 4sqrt6$

Answer 2 · 2016-02-17T14:05:45

$A r e a = 4 \sqrt{6} . u n i t s$ $Area=4sqrt6.units$

Explanation:

$A = A r e a$ $A=Area$

$a - b - c = s i d e s$ $a-b-c=sides$

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

Heron's formula for the area of the triangle:

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

In this case $a = 4, b = 5, c = 7, s = \frac{4 + 5 + 7}{2} = \frac{16}{2} = 8$ $color(green)(a=4,b=5,c=7,s=(4+5+7)/2=16/2=8$

$\to A = \sqrt{8 (8 - 4) (8 - 5) (8 - 7)}$ $rarrA=sqrt(8(8-4)(8-5)(8-7))$

$\to A = \sqrt{8 (4) (3) (1)}$ $rarrA=sqrt(8(4)(3)(1))$

$\to A = \sqrt{8 (12)}$ $rarrA=sqrt(8(12))$

$\Rightarrow A = \sqrt{96} = \sqrt{16 \cdot 6} = 4 \sqrt{6}$ $rArrcolor(orange)(A=sqrt96=sqrt(16*6)=4sqrt6$

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A triangle has sides with lengths: 4, 5, and 7. How do you find the area of the triangle using Heron's formula?

2 Answers

Explanation:

Explanation:

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