Question

the area of the rectangular face of a uniform triangular prism is 60 CM square and the perimeter of the triangle of Asus is 18 cm what is the volume of the prism in centimetre cube​

Answer 1

Given :- The area of the rectangular face of a uniform triangular prism is 60cm² and the perimeter of the triangular faces is 18 cm. what is the volume of the prism in cm³ ?

Solution :-

we have ,

→ Perimeter of uniform triangular faces is = 18 cm.

So,

→ Each sides of triangular faces is = (18/3) = 6 cm.

then,

→ Area of the rectangular face = side of the triangular face * Height of the prism.

→ 60 cm² = 6 cm * Height

→ Height = (60/6) = 10 cm.

therefore,

→ Volume of Prism = (Area of Base of triangular faces) * Height of Prism .

→ Volume of Prism = {√3/4 * (side)²} * 10 cm .

→ Volume of Prism = {(√3/4) * (6)²} * 10

→ Volume of Prism = (√3/4) * 36 * 10

→ Volume of Prism = √3 * 9 * 10

→ Volume of Prism = 90√3 cm³ . (Ans.)

Hence, the volume of the prism is 90√3 cm³.

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