Question

Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.

Answer 1

Answer :

Base is 12cm.

Hypotenuse is 13cm.

Hypotenuse^2 = Base^2 + Height^2 =>

13*13 = 12*12 + Height^2 => 169-144 =25 =>

Height =√25 = 5cm . So Area of the right angled triangle = 1/2*Base*height =1/2*12*5 = 30 square centimetre. Hope it helps you .

Answer 2

Solution

Given :

Base = 12 cm

Hypotenuse = 13 cm

                                               

To find :

Area of right angled triangle

                                               

Let XYZ be the given triangle

with XZ = 13 cm and YZ = 12 cm.

                                               

Here we use Pythagoras theorem

                                               

By Pythagoras theorem,

⇒ (XZ)² = (XY)²  +  (YZ)²

⇒ (13)²    =   (XY)²  +  (5)²

⇒ (13)² - (12)²  = (XY)²

⇒ 169 - 144 = (XY)²

⇒ 25 = (XY)²

⇒ XY = 5

                                               

Now we are going to find

area of triangle XYZ

                                               

Area of triangle = 1/2 × Base × Height

                                               

Area of ΔXYZ =

= $\dfrac{1}{2}\times Base\times Height\\\\\\\implies\dfrac{1}{2}\times12\:cm\times5\\\\\\=6\:cm\times5\:cm\\\\\\=30\:cm^2$

                                               

Therefore area of right-angled

triangle is 30 cm² whose base is

12 cm and hypotenuse is 13 cm