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Chapter 12: Q17. (page 478)

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

Equilateral triangle with side 8, h = 10.

Short Answer

Expert verified

The lateral area is 240, the total area is(240+323) and the volume is1603 .

Step by step solution

01

Step 1. Given information.

The side of equilateral triangle is 8 and height is 10.

02

Step 2. Write the concept.

The lateral area of the equilateral triangular prism is given by:

L.A.=3(Side脳Height)

The total area of the equilateral triangular prism is given by:

T.A.=L.A.+2(34Side2)

The volume of equilateral triangular prism is given by:

V=34(side)2脳h

03

Step 3. Sketch the graph.

Now to draw a prism first make its base as a triangle and then sketch the length of 10 triangle from its each point,

Thus, the prism can be obtained as:

04

Step 4. Determine values.

The lateral area is:

L.A.=3(Side脳Height)=3(8脳10)=3脳80=240鈥夆赌塽苍颈迟2

The total area is:

T.A.=L.A.+2(34Side2)=240+32(8)2=240+32脳64=(240+323)unit2

And the volume is:

V=34(side)2脳h=34(8)2脳10=6434脳10

So,

V=163脳10=1603鈥夆赌塽苍颈迟3

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