Question

a field is in the form of a right triangle with hypotenuse 50 m and one of the perpendicular sides is 40m.find the area of the field.

Answer 1

First you need to find the base of the right angle triangle by using Pythagoras theorem that is H^2=B^2+P^2 and then use the formula of area of the triangle that is 1/2×base×hight

Answer 2

$\bf{We\:know\::\:}\rm{Area\:of\:Triangle\:=\:\dfrac{1}{2}\times Height\times Base}$

• In A Right Angled Triangle, The Sides Except Hypotenuse are known as Height and Base

To Find Base, We use Pythagoras Theorem :

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of height and base sides“

(Hypotenuse)² = (Height)² + (Base)²

⇒ (50 m)² = (40 m)² + (Base)²

⇒ 2500 m² = 1600 m² + (Base)²

⇒ 2500 m² - 1600 m² = (Base)²

⇒ 900 m² = (Base)²

⇒ Base = 30 m

Now, Time To Calculate Area of Triangle !!

$\rm{Area\:of\:Triangle\:=\:\dfrac{1}{2}\times Height\times Base}$

$\to\rm{Area\:of\:Triangle\:=\:\dfrac{1}{2}\times 40 m\times 30 m}$

$\to\rm{Area\:of\:Triangle\:=\:20 m\times 30 m}$

$\to\underline{\underline{\rm{Area\:of\:Triangle\:=\:600 m^2}}}$