Question

Find the missing values: [3 MARKS]

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

Answer 1

Each Blank: 1 Mark

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

Thus, the missing values are:
$$\begin{array}{ccc}\text{Base}& \text{Height}& \text{Area of triangle}\\ 15cm& 11.6cm& 87c{m}^2\\ 80mm& 31.4mm& 1256m{m}^2\\ 22cm& 15.5cm& 170.5c{m}^2\end{array}$$