Question

Find the missing values:

Base	Height	Area of triangle
$15$ cm	______	$87c{m}^2$
________	$31.4$ mm	$1256$ $m{m}^2$
$22$ cm	_______	$170.5$ $c{m}^2$.

Answer 1

We know that the area of triangle$=\frac{1}{2}\times$base$\times$height
In first row, base$=15$cm and area$=87$ $c{m}^2$
$\therefore 87=\frac{1}{2}\times 15\times$ height
$\Rightarrow$ height$=\frac{87\times 2}{15}=11.6$cm
In second row, height$=31.4$mm and area$=1256$ $m{m}^2$
$\therefore 1256=\frac{1}{2}\times$base$\times 31.4$
$\Rightarrow$base$=\frac{1256\times 2}{31.4}=80$mm
In third row, base$=22$ cm and area$=170.5$ $c{m}^2$
$\therefore 170.5=\frac{1}{2}\times 22\times$height
$\Rightarrow$ height$=\frac{170.5\times 2}{22}=15.5$cm
Thus, the missing values are:

Base	Height	Area of triangle
$15$ cm	$11.6$ cm	$87$ $c{m}^2$
$80$ mm	$31.4$ mm	$1256$ $m{m}^2$
$22$ cm	$15.5$ cm	$170.5$ $c{m}^2$