What is the area of a triangle with sides 10, 10 and 16?

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What is the area of a triangle with sides 10, 10 and 16?

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Answer 1 · 2015-06-01T12:24:45

The height of a triangle with sides 10, 10, and 16, if we use 16 as the base is 6 (Pythagorean Theorem and diagram below).

Therefore the area of the triangle is
$A = \frac{1}{2} b h = \frac{1}{2} \cdot 16 \cdot 6 = 48$ $A=1/2bh = 1/2*16*6 = 48$
enter image source here

Alternately you could use Heron's formula
$A = \sqrt{s (s - a) (s - b) (s - c)}$ $A=sqrt(s(s-a)(s-b)(s-c))$ for a triangle with sides $a, b, and c$ $a, b, and c$ and a semi-perimeter of $s$ $s$ .

In this case $s = 18$ $s=18$
and
the area $= \sqrt{18 (8) (8) (2)} = \sqrt{36 \cdot 8^{2}} = 6 \cdot 8 = 48$ $=sqrt(18(8)(8)(2)) = sqrt(36*8^2) = 6*8 = 48$

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What is the area of a triangle with sides 10, 10 and 16?

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