Squares, Rectangles, and Parallelograms

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GED Math › Squares, Rectangles, and Parallelograms

Questions 1 - 10
1

If the area of square is , what is its perimeter?

Explanation

Figuring out the perimeter of a square from this information is luckily pretty easy. Since the sides of a square are all the same size, you know also that .

Taking the square root of both sides, you get:

Now, the perimeter of the square is just , or .

2

A square and a circle share a center as shown by the figure below.

1

If the length of a side of the square is and is half the length of the radius of the circle, to the nearest hundredths place, find the area of the shaded region.

Explanation

In order to find the area of the shaded region, we will need to find the area of the circle then subtract the area of the square from it.

Start by finding the area of the square. Since we know the side length of the square, we can write the following:

Next, we find the area of the circle. Since the question states that the length of a side of the square is half the radius of the circle, the radius of the circle must be . Thus, we can find the area of the circle.

Now, subtract these two values to find the area of the shaded region.

3

A rectangle has length 10 inches and width 5 inches. Each dimension is increased by 3 inches. By what percent has the area of the rectangle increased?

Explanation

The area of a rectangle is its length times its width.

Its original area is square inches; its new area is square inches. The area has increased by

.

4

Find the area of a square with a side of .

Explanation

Write the formula for the area of a square.

Substitute the side.

The answer is:

5

Find the area of a square with a side of .

Explanation

Write the formula for the area of a square.

Substitute the side.

The answer is:

6

A square and a circle share a center as shown by the figure below.

1

If the length of a side of the square is and is half the length of the radius of the circle, to the nearest hundredths place, find the area of the shaded region.

Explanation

In order to find the area of the shaded region, we will need to find the area of the circle then subtract the area of the square from it.

Start by finding the area of the square. Since we know the side length of the square, we can write the following:

Next, we find the area of the circle. Since the question states that the length of a side of the square is half the radius of the circle, the radius of the circle must be . Thus, we can find the area of the circle.

Now, subtract these two values to find the area of the shaded region.

7

If the area of square is , what is its perimeter?

Explanation

Figuring out the perimeter of a square from this information is luckily pretty easy. Since the sides of a square are all the same size, you know also that .

Taking the square root of both sides, you get:

Now, the perimeter of the square is just , or .

8

A rectangle has length 10 inches and width 5 inches. Each dimension is increased by 3 inches. By what percent has the area of the rectangle increased?

Explanation

The area of a rectangle is its length times its width.

Its original area is square inches; its new area is square inches. The area has increased by

.

9

If the perimeter of a square is , what is its area?

Explanation

Since the four sides of a square are equal, you know that the perimeter of a square is defined as:

For our data, this is:

Solving for , you get:

Now, the area of a square is just:

or , which is the same as .

10

If a square has a length of 10in, find the area.

Explanation

To find the area of a square, we will use the following formula:

where l is the length and w is the width of the square.

Now, we know the length of the square is 10in. Because it is a square, all sides are equal. Therefore, the length is also 10in. So, we can substitute. We get

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