Question

The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. Find
its area

Answer 1

semi perimeter = (10+13+13)/2 = 18
area = √{18(18-10)(18-13)(18-13)}
= √(18×8×5×5)
= √(2×3×3×2×2×2×5×5)
=2×2×3×5
=60

Answer 2

Area of the isosceles triangle $\bold{=60\ cm^2}$  

Given:  

Base = 10 cm

One of the equal side = 13 cm

To find:  

Area = ?

Solution:  

The formula for area of isosceles triangle $=\frac{1}{2} \times b \times h$ square units

As the height is not given to find that divide the isosceles triangle in to two right angle triangle then by using Pythagoras s theorem we can find the height of the triangle.  

To find the height of the given triangle.

Using Pythagoras theorem,  

$h=\sqrt{13^{2}-5^{2}}=\sqrt{169-25}=\sqrt{144}=12\ \mathrm{cm}$

Substituting base and height in formula  

$=\frac{1}{2} \times 10 \times 12=\frac{120}{2}=60\ \mathrm{cm}^{2}$

Therefore the area of the isosceles triangle is $60\ \mathrm{cm}^{2}$.