Question

$\begin{array}{ccc}\text{Base}& \text{Height}& \text{Area of Triangle}\\ 15cm& \dots & 87c{m}^2\\ \dots & 31.4mm& 1256m{m}^2\\ 22cm& \dots & 170.5c{m}^2\end{array}$

Find the missing values.

Answer 1

(1) Base, $b=15cm$

$h=?$
Area of Triangle, $A=87c{m}^2$
For triangle,
$\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$

$A=\frac{1}{2}b\times h$
$⟹87c{m}^2=\frac{1}{2}\times 15\times h$

$⟹\frac{15h}{2}=87$

$⟹h=\frac{87\times 2}{15}$
$⟹h=\frac{58}{5}=11.6$
Hence, height, $h=11.6cm$

(2) Base, $b=?$

Height, $h=31.4mm$

Area of Triangle, $A=1256m{m}^2$
For triangle,
$A=\frac{1}{2}\times b\times h$

$⟹1256=\frac{1}{2}\times b\times 31.4$
$⟹1256=\frac{31.4b}{2}$
$⟹1256=15.7b$
$⟹b=\frac{1256}{15.7}$
$⟹b=80$

$\therefore b=80mm$
Hence, base, $b=80mm$

(3) Base, $b=22cm$

Height, $h=?$

Area of Triangle, $A=1705c{m}^2$
For triangle,

$A=\frac{1}{2}\times b\times h$
$⟹1705=\frac{1}{2}\times 22\times h$
$⟹1705=\frac{22h}{2}$
$⟹1705=11h$
$⟹h=\frac{1705}{11}$

$⟹h=15.5$

Hence, height, $h=15.5cm$