Question

base of right-angled triangle measures 6 cm and its hypotenuse is 10 cm. The semi perimeter is​

Answer 1

Here, we are given that

Base = 4cm

Hypotenuse = 5cm

Area of a triangle = 1/2 × base × height.

Height is not given

In a right triangle, the height is the third side apart from base and hypotenuse. So by Pythagoras Theorem, we can find the third side . We know that,

h² = b² + p²

Where h = hypotenuse, b = base and p = perpendicular (height)

So, p² = h² - b²

=> p² = 5² - 4²

=> p² = 25 - 16

=> p² = 9

=> p = √9

=> p = 3cm

So the perpendicular (height) is 3 cm

So area = 1/2 × base × height

=> 1/2 × 4 × 3

=> 2 × 3

= 6 cm²

Your answer :- 6cm