# Area vs. Surface Area in Geometry

## What is Area?

Area is a measure of the two-dimensional size of a flat shape or surface. It is a measure of the amount of space occupied by a flat shape or surface. Area is usually measured in square units, such as square feet or square meters. The area of a shape is the total number of square units inside the shape. For example, the area of a square can be calculated by multiplying the length of one side by itself.

Area is an important concept in geometry, as it is used to calculate the size of many different shapes. It can also be used to calculate the area of a region, such as a state or country. For example, the area of the United States is approximately 3,805,927 square miles.

## What is Surface Area?

Surface area is a measure of the three-dimensional size of a solid shape or object. It is a measure of the total area of the surfaces of a solid object. Surface area is usually measured in square units, such as square feet or square meters. The surface area of a shape is the total number of square units on the surface of the shape.

Surface area is an important concept in geometry, as it is used to calculate the size of many different three-dimensional shapes. It can also be used to calculate the surface area of a region, such as a country or continent. For example, the surface area of the United States is approximately 9,833,520 square miles.

## How are Area and Surface Area Different?

Area and surface area are related concepts, but they are not the same. Area measures the two-dimensional size of a flat shape or surface, while surface area measures the three-dimensional size of a solid object. Area is usually measured in square units, while surface area is usually measured in cubic units.

A good way to differentiate between area and surface area is to think of area as the size of the inside of a shape, and surface area as the size of the outside of a shape. For example, the area of a square is the total number of square units inside the shape, while the surface area of a cube is the total number of square units on the surface of the cube.

Area and surface area are also related to the concept of volume. Volume is a measure of the three-dimensional size of a solid shape or object. It is a measure of the amount of space occupied by a solid object. Volume is usually measured in cubic units, such as cubic feet or cubic meters. The volume of a shape is the total number of cubic units inside the shape.

## Practice Problems

1. Find the area of a triangle with sides of length 4 cm, 5 cm, and 6 cm.

Answer: 12 cm^{2}

2. Find the surface area of a cube with sides of length 5 cm.

Answer: 150 cm^{2}

3. Find the volume of a rectangular prism with length 8 cm, width 6 cm, and height 5 cm.

Answer: 240 cm^{3}

4. Find the area of a circle with a radius of 3 cm.

Answer: 28.27 cm^{2}

5. Find the surface area of a sphere with a radius of 4 cm.

Answer: 201.06 cm^{2}

6. Find the area of a trapezoid with bases of 7 cm and 5 cm, and a height of 6 cm.

Answer: 36 cm^{2}

7. Find the surface area of a pyramid with a base of 10 cm and a height of 8 cm.

Answer: 160 cm^{2}

8. Find the volume of a cylinder with a radius of 5 cm and a height of 10 cm.

Answer: 785.4 cm^{3}

## Summary

In this article, we discussed the difference between area and surface area in geometry. Area is a measure of the two-dimensional size of a flat shape or surface, while surface area is a measure of the three-dimensional size of a solid shape or object. Area is usually measured in square units, while surface area is usually measured in cubic units. Area is related to the concept of volume, which is a measure of the three-dimensional size of a solid shape or object. We also provided several practice problems with answers to help illustrate the concepts discussed.

## FAQ

### What does surface area mean in geometry?

Surface area is the collective measure of the areas of all of the faces of a three-dimensional object. It is the sum of the areas of the faces of a three-dimensional object, such as a cube or a sphere.

### What is the difference between surface area and lateral area?

Surface area is the measure of all the faces of a three-dimensional object, while lateral area is the measure of only its sides. Surface area includes the top and bottom faces, while lateral area does not.

### What is the difference between surface area and area and volume?

Surface area is the measure of the total surface of a three-dimensional object, while area is the measure of a two-dimensional shape. Volume is the measure of the amount of space taken up by a three-dimensional object.

### What is the difference between surface and?

Surface is the measure of the total surface of a three-dimensional object, while area is the measure of a two-dimensional shape.