A parallelogram and a triangle have the same base and equal areas. If the sides of triangle are 18 cm, 24 cm and 30 cm and their common base is 30 cm, find height of the parallelogram.
Answers
Step-by-step explanation:
If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Given :
• A parallelogram and a triangle have the same base and equal areas.
• The three sides of triangle :-
- First side = 18 cm
- Second side = 24 cm
Third side = 30 cm
• The common base of parallelogram and triangle is 30 cm
To find :
• Height of the parallelogram
Solution :
Firstly, we will calculate the area of triangle by using the Heron's formula.
⟶ Semi perimeter of the triangle = (a + b + c) ÷ 2
where,
- a, b and c are the three sides of the triangle
Substituting the given values :-
⟶ Semi perimeter = (18 + 24 + 30) ÷ 2
⟶ Semi perimeter = 72 ÷ 2
⟶ Semi perimeter = 36
Therefore, the semi perimeter of the triangle = 36 cm
⟶ Heron's formula = √s(s - a)(s - b)(s - c)
where,s is the semi perimeter of the triangle
Substituting the given values :-
⟶ Area of triangle = √36(36 - 18)(36 - 24)(36 - 30)
⟶ Area of triangle = √36(18)(12)(6)
⟶ Area of triangle = √36(1296)
⟶ Area of triangle = √46,656
⟶ Area of triangle = 216
Therefore, the area of triangle = 216 cm²
⟶ Area of triangle = Area of parallelogram
Hence, Area of parallelogram = 216 cm²
Using formula,
⟶ Area of parallelogram = b × h
where,
- b = base of the parallelogram
- h = height of the parallelogram
Substituting the given values :-
⟶ 216 = 30 × h
⟶ 216/30 = h
⟶ 7.2 = h
Therefore, the height of the parallelogram = 7.2 cm