Question

Calculate the area of an isosceles triangle if the equal sides are 16cm each and the unequal side is 10cm.(without using heron's formula) [2 MARKS]

Answer 1

Concept : 0.5 Mark
Application : 0.5 Mark
Calculation : 1 Mark

From X we draw a perpendicular XP to side YZ. We can see that this perpendicular XP divides the base YZ of the triangle in two equal parts.

Therefore, YP = PZ =$\frac{1}{2}$ YZ = 5 cm

Then, by using Pythagoras theorem, we get

$X{P}^2$ = $X{Y}^2$ – $Y{P}^2$

= ${16}^2$ – $5^2$ = 256 – 25 = 231

So, XP = $\sqrt{231}$ cm

Now, area of $\Delta$XYZ =$\frac{1}{2}$ × base YZ × height XP

=$\frac{1}{2}$ × 10 × $\sqrt{231}$ $c{m}^2$ = 5 $\sqrt{231}$ $c{m}^2$