Question

The base and altitude of a parallelogram ate respectively 12cm and 18cm and the area of parallelogram is equal to the area of the triangle whose base is 54cm. Find the height of the triangle

Answer 1

Answer:-

Given:

Base of a Parallelogram = 12 cm.

Altitude of the Parallelogram = 18 cm.

Base of a Triangle = 54 cm.

And,

Area of the Parallelogram = Area of Triangle.

According to the question,

Base (Parallelogram) * Height (Parallelogram) = 1/2* Base (Triangle).

→ 12*18 = 1/2 * 54 * Height (Triangle)

→ 12*18*2/54 = Height

→ Height = 8 cm.

Therefore, the height of the triangle is 8 cm.

Answer 2

✬ Height of Triangle = 8 cm ✬

Given:

• Area of parallogram = Area of the triangle
• Base and altitude of the parallogram is 12 cm and 18 cm.
• Length of base of triangle is 54 cm.

To Find:

• What is the measure of height of the parallogram?

Formula to be used:

• Area of parallogram = Base x Height
• Area of triangle= 1/2 x Base x Height

Solution: Since, the parallogram and triangle both have equal areas. Therefore,

$\implies{\rm }$ Base x Height = 1/2 x Base x Height

$\implies{\rm }$ ( 12 x 18 ) = ( 1/2 x 54 x Height )

$\implies{\rm }$ 216 =( 27 x Height )

$\implies{\rm }$ 216/27 = Height

$\implies{\rm }$ 8 cm = Height

Hence, The height of triangle is of 8 cm.

____________________

★ Check ★

→ Base x Height = 1/2 x Base x Height

→ (12 x 18) cm² = (1/2 x 54 x 8) cm²

→ 216 cm² = (27 x 8) cm²

→ 216 cm² = 216 cm² { LHS = RHS }

Hence, Both areas are equal.