find the area of an isosceles triangle whose perimeter is 32cm and its base is 12cm
Answers
The area of the triangle is 48 cm².
Explanation:
It is given that,
The perimeter of the isosceles triangle = 32 cm
The base of the triangle = 12 cm
∴ The sum of the equal sides of the triangle = (32-12) cm
= 20 cm
∴ The length of each equal side = (20/2) cm
= 10 cm
Now, imagine a perpendicular through the mid-point of the triangle such that it bisects the base.
∴ We get 2 right-angled triangles.
For each equal triangle_
Hypotenuse = 10 cm
Base = (12/2) cm
= 6 cm
∴ Height = √hypotenuse² - base² [∵ Pythagoras theorem.]
= √(10)² - (6)²
= √100 - 36
= √64
= 8 cm
∴ For the isosceles triangle we get,
Height = 8 cm
∴ Area = (Base × Height)/2
= (12 ×8)/2 cm²
= (96/2) cm²
= 48 cm²
∴ The area of the triangle is 48 cm².
#answerwithquality
#BAL
Answer:
Answer:here is your answer... I hope it will be help you
