Question

Base of a prism is an isosceles right angled triangle with
hypotenuse 18 cm. If height of prism is 3.5 cm. Find the
volume of the prism.
(A) 2112 cm
(B) 243V2cm
(0) 64/2 cm
(D) 343 cm​

Answer 1

Answer:

I don't know ask another one

Answer 2

Answer:

The hypotenuse of the right-angled triangle = 18 cm

Height of the prism = 3.5 cm

Step 1: finding the area of the base of the isosceles right-angled triangle prism

Since the base is an isosceles right-angled triangle, therefore two of its sides are equal i.e., length = base.

Using Pythagoras theorem for the triangle, we have

Hypotenuse² = length² + base²

⇒ 18² = 2 * length²

⇒ length = √[324/2] = √[162] = 9√2 cm

∴ length = base = 9√2 cm

Here, length = height of the triangle

∴ The area of the base is,  

= ½ * base * height  

= ½ * 9√2 * 9√2  

= 81 cm²

Step 2: finding the volume of the prism

Thus,  

The volume of the prism is,

= [Area of the base of the isosceles right-angled triangle prism] * [height]

= 81 * 3.5

= 283.5 cm³