Volume of prism base area 12 length 5 Easy

The question

Question: find the volume of a prism with base area 12 square units and length 5.

1 Base times length

A prism has the same shape all the way through.

The face at the end is the base.

Its area is A = 12 square units.

The prism is that base, stacked up 5 long.

Like the circle of a cylinder.

So the volume is V = A × length.

Now put the numbers in: A = 12 and length = 5.

12 times 5 is 60.

So the volume is 60 cubic units.

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Volume of triangular prism base 5 height 3 length 4 Medium

The question

Question: find the volume of a triangular prism with triangle base 5 and height 3, and length 4.

1 Area of the base

A prism has the same shape all the way through.

Here it is a triangle.

The triangle is the base.

Careful: the prism lies on its side.

Its base is the triangle at the end, not the face it lies on.

The triangle is half of the box around it.

So its area is half of base times height: A = ½ × 5 × 3.

5 times 3 is 15.

That is the whole box.

Half of 15 means 15 divided by 2.

That is 7.5.

So the base is A = 7.5 square units.

2 Base times length

The prism is that triangle, stacked up 4 long.

So the volume is V = A × length.

Now put the numbers in: A = 7.5 and length = 4.

Forget the points: 75 times 4 is 300.

The numbers have 1 digit after the point.

So the answer has 1 too: 30.0, which is 30.

So the volume is 30 cubic units.

Let's look back.

First: area of the base.

Last: base times length.

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Surface area of triangular prism base 6 height 4 sides 5 length 10 Harder

The question

Question: find the surface area of a triangular prism with triangle base 6, height 4 and sides 5, and length 10.

1 Count the faces

The surface area is the area of all the outside faces.

This prism has 5 faces: 2 triangles and 3 rectangles.

2 The two triangles

The triangle has base 6 and height 4.

One triangle is half of base times height: ½ × 6 × 4.

6 times 4 is 24.

Half of 24 means 24 divided by 2.

That is 12.

So one triangle is 12 square units.

The back is the same.

Two triangles: 2 times 12 is 24.

3 The three rectangles

The bottom rectangle is 6 by 10.

This one is 5 by 10.

And this one is 5 by 10.

Unroll the three rectangles side by side.

They make one long rectangle: 6 + 5 + 5 wide and 10 long.

So the rectangles are around the triangle, times the length.

6 plus 5 plus 5 is 16.

16 times 10 is 160.

So the rectangles are 160 square units.

4 Add all the faces

Add the triangles and the rectangles: 24 + 160.

24 plus 160 is 184.

So the surface area is 184 square units.

Let's look back.

First: count the faces.

Then: the two triangles.

Then: the three rectangles.

Last: add all the faces.

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