An triangle has perimeter 32 cm and two sides of which are 8 cm and 11 cm. Find
the area of the triangle.
Answers
Answer:
8√30cm²
Step-by-step explanation:
let the sides of the triangle be a, b and c
given length of the sides of the triangle are :-
a = 8cm
b = 11cm
c = ?
perimeter of the triangle is given = 32cm
since the sum of all three sides of a triangle is it's perimeter
=> a + b + c = 32cm
=> 8 + 11 + c = 32cm
=> 19 + c = 32cm
=> c = 32 - 19
=> c = 13cm
now we will find the area of the triangle by heron's formula which is √s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle.
semi-perimeter of this triangle = 32/2
= 16cm
area of the triangle = √16(16-8)(16-11)(16-13)
= √(16 × 8 × 5 × 3)
= √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3)
= 2 × 2 × 2√(2 × 5 × 3)
= 8√30cm²
Step-by-step explanation:
Third side = 32-(8+11) = 32-19 = 13
Area of triangle
=