Question
Download Solution PDFThe base of a prism is a right angled isoceles triangle whose hypotenuse is 3√2 cm. If the height of the prism is 12 cm, find the volume of the prism?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Hypotenuse of base triangle = 3√2 cm
Height of prism = 12 cm
Formula used:
In a right angled triangle;
(Hypotenuse)2 = (Base)2 + (Height)2
Area of triangle = (1/2) × Base × Height
Volume of Prism = Area of base × Height
Calculation:
In Isoceles triangle; two sides are equal.
Let the equal sides = a cm
(3√2)2 = a2 + a2
⇒ 18 = 2a2
⇒ a2 = 9 cm2
⇒ a = 3 cm
Area of triangular base = (1/2) × 3 × 3
⇒ 9/2 cm2
Volume of Prism = 12 × (9/2) cm3
⇒ 54 cm3
∴ The volume of prism is 54 cm3.
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