# HiSET: Math : Area

## Example Questions

### Example Question #31 : Measurement And Geometry

Find the area of a square with the following side length:

Explanation:

We can find the area of a circle using the following formula:

In this equation the variable, , represents the length of a single side.

Substitute and solve.

### Example Question #91 : Hi Set: High School Equivalency Test: Math

The perimeter of a square is . In terms of , give the area of the square.

Explanation:

Since a square comprises four segments of the same length, the length of one side is equal to one fourth of the perimeter of the square, which is . The area of the square is equal to the square of this sidelength, or

.

### Example Question #1 : Area

The volume of a sphere is equal to . Give the surface area of the sphere.

None of the other choices gives the correct response.

Explanation:

The volume of a sphere can be calculated using the formula

Solving for :

Set . Multiply both sides by :

Divide by :

Take the cube root of both sides:

Now substitute for in the surface area formula:

,

the correct response.

### Example Question #21 : Properties Of Polygons And Circles

Express the area of a square plot of land 60 feet in sidelength in square yards.

600 square yards

200 square yards

600 square yards

400 square yards

3,600 square yards

400 square yards

Explanation:

One yard is equal to three feet, so convert 60 feet to yards by dividing by conversion factor 3:

Square this sidelength to get the area of the plot:

,

the correct response.

### Example Question #1 : Area

A square has perimeter . Give its area in terms of .

Explanation:

Divide the perimeter to get the length of one side of the square.

Divide each term by 4:

Square this sidelength to get the area of the square. The binomial can be squared by using the square of a binomial pattern:

### Example Question #1 : Area

A cube has surface area 6. Give the surface area of the sphere that is inscribed inside it.