Question

Find the missing values:

Base	Height	Area of triangle
15 cm	-	87 $cm^2$
-	31.4 mm	1256 $mm^2$
22 cm	-	170.5 $cm^2$

Answer 1

$\text{Area of a triangle}=\frac{1}{2}\times\text{Base}\times\text{Height}$
(a) $b = 15 \;cm$
$h=?$

$Area = \frac{1}{2}\times b\times h=87\; cm^2$

$\frac{1}{2}\times15\times h=87\;cm^2$

$h= \frac{87\times2}{15}=11.6\;cm^2$

Therefore, the height of such triangle is $11.6$ $cm$.

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(b) $b = ?$
$h=31.4\; mm$

$Area=\frac{1}{2}\times b\times h=1256 \; mm^2$

$b = \frac{1256\times2}{31.4}=80\; mm$

Therefore, the base of such triangle is $80$ $mm$.

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(c) $b = 22 \;cm ,\;h = ?$

$Area=\frac{1}{2}\times b\times h=170.5\; cm^2$

$\frac{1}{2}\times 22\times h=170.5\;cm^2$

$h=\frac{170.5\times2}{22}=15.5\;cm$

Therefore, the height of such triangle is $15.5$ $cm$.