Question

The height of an equilateral rectangular prism increases by four units. The new lateral area is more than the original by how much? Show and explain.

Answer 1

Choices: four more than the perimeter of the base

four times the the area of the base

four times the perimeter of the base

four more than the area of the base

Answer 2

So can we start it now??

Answer 3

The Lateral Area of Rectangular Prism is given by:

\[\color{green}{Lateral_{Area} = (Perimeter \; of\; Base) \times Height}\]

Answer 4

Here Height is increased by 4..

For Simplicity I am Writing Height as H..

See earlier it was H..

But now height gets increased by 4, so it has now become:

(H + 4)

Can you substitute it in the formula in place of H???

Answer 5

I dont get it

Answer 6

Okay reply fast if you don't get it..

Suppose,

earlier height was H.

Now height gets increased by 4 so it has become:

H + 4

Understood??

Answer 7

Four more than the perimeter of base?

Answer 8

You can think it as:

Suppose @Mastercat your age is 16 years..

After four it year it will get increased by 4 :

16 + 4


But in our case we are not given Height value So let it be H..


After increased by 4 it will become H + 4..

Answer 9

Yes absolutely right....

Answer 10

I see it now.

Answer 11

See,

\[LA = (BP) \times (H+4)\]

where BP is Base Perimeter and H is height..

\[LA = (BP) \times (H) + \color{green}{(BP) \times (4)}\]

Look for green part..

Answer 12

earlier it was:
\[LA = (BP) \times (H)\]

by how much it has got increased??

The green part is saying that..

Answer 13

Getting what I have shown???

Answer 14

@waterineyes so the area of the base is four times what it originally was