Calculate Base Area of Orthohedron: Given Volume 80 cm³ and 4m Edge

Look at the following orthohedron:

444

The volume of the orthohedron is 80 cm3 80~cm^3 .

The length of the lateral edge is 4 meters.

What is the area of the base of the orthohedron?
(shaded orange in the diagram)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the base area
00:03 The base area equals the box length multiplied by its width
00:24 The base area is a rectangle therefore all angles are right angles
00:28 We'll use the formula for calculating box volume
00:32 Width multiplied by height multiplied by length
00:35 Insert the appropriate values into the formula according to the given data and solve in order to find the area
00:46 Our aim is to determine the product of the height and width together
01:03 Let's isolate the area
01:06 Here is the solution

Step-by-step written solution

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1

Understand the problem

Look at the following orthohedron:

444

The volume of the orthohedron is 80 cm3 80~cm^3 .

The length of the lateral edge is 4 meters.

What is the area of the base of the orthohedron?
(shaded orange in the diagram)

2

Step-by-step solution

The formula for the volume of a box is height*length*width

In the specific question, we are given the volume and the height,

and we are looking for the area of the base,

As you will remember, the area is length * width

If we replace all the data in the formula, we see that:

4 * the area of the base = 80

Therefore, if we divide by 4 we see that

Area of the base = 20

3

Final Answer

20 cm²

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

121212888555

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