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find the area of the triangle, carry your internediate computations to at least four decimal places round your answer to the nearest tenth

Find The Area Of The Triangle Carry Your Internediate Computations To At Least Four Decimal Places Round Your Answer To The Nearest Tenth class=

Sagot :

Heron's formula is defined as:

[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where} \\ a,b,\text{ and }c\text{ are the three sides of the triangle} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]

Given: sides with length 12 yd, 14 yd, 15 yd.

Then

[tex]\begin{gathered} s=\frac{12+14+15}{2} \\ s=\frac{41}{2} \\ s=20.5\text{ yd} \end{gathered}[/tex]

Plugin the following values to Heron's formula and we get

[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{20.5(20.5-12)(20.5-14)(20.5-15)} \\ A=\sqrt[]{20.5(8.5)(6.5)(5.5)} \\ A=78.926785694085\text{ yd}^2 \\ \text{Rounded this off to the nearest tenth and we get} \\ A=78.9\text{ yd}^2 \end{gathered}[/tex]

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