Area and Perimeter Math Problems and Solutions

What are Area and Perimeter?

Students likely will work with the area and perimeter of shapes throughout high school; however, early studies usually begin in third grade with simple, 2-dimensional shapes like squares, rectangles and parallelograms. Before working with your child on these concepts, you'll want to make sure he or she understands the difference. Area, which is measured in square units, is the amount of surface space taken up by a 2-D shape. It's calculated by multiplying the length of a shape by its width. Perimeter is the distance around the outside of a 2-D shape. It's measured by adding the lengths of all of a shape's sides.

It may be helpful to illustrate these concepts for your child. For example, to demonstrate area, you might draw a shape and have your child color in the inside, or area, of it. To depict perimeter, you could draw another shape and have your child outline the sides.

While your child's teacher can be an excellent resource for extra practice worksheets, you also can develop your own area and perimeter problems at home. You might use the following examples as your guide.

Math Problems by Concept

Area of a Square

What is the area of a square with 4-inch sides?

To solve this problem, your child should multiply the length of the square by its width. Since both are 4 inches, the answer is 16 square inches. It might be helpful to your child if you provide a drawing of a square and label each side.

Area of a Rectangle

A rectangle has a width of 4 inches and a height of 10 inches. What is the rectangle's area?

Like the first problem, the area is calculated by multiplying the width, 4 inches, by the height, 10 inches. The rectangle has an area of 40 square inches.

Perimeter of a Square

What is the perimeter of a square with 5-inch sides?

To calculate perimeter, your child should add all the sides together. Because the sides of a square are equal, the equation for this problem would be 5 + 5 + 5 + 5 = 20. The perimeter of the square is 20 inches.

Perimeter of a Rectangle

A rectangle is 7 inches wide and 3 inches high. What is the perimeter?

Again, all the sides should be added together, so the equation might look like this: 7 + 7 + 3 + 3 = 20. The rectangle's perimeter is 20 inches.