 # Elementary Math Formulas, Solutions and Explanations

Although formulas are an important component of mathematics study in middle and high school, they're typically not a big part of elementary math. However, your child likely will be introduced to a handful of formulas - including those for perimeter, area and volume - by the time he or she completes fifth grade. ## What Elementary Math Formulas Does My Child Need To Know?

In third and fourth grades, students learn to calculate the perimeter and area of 2-dimensional shapes, including squares, rectangles and triangles, and in fifth grade, they move on to determining the volume of cubes and rectangular prisms. In some cases, students may be required to memorize the formulas for these calculations; in others, the teacher may provide students with these formulas for assignments and tests. As you review the sample problems below, keep in mind that many formulas use notations like 'l' for length, 'w' for width, 'h' for height and 'b' for base.

## Formulas and Sample Problems

### Perimeter

The perimeter (P) of a shape can be calculated by adding together the lengths of all its sides. Although the formula for perimeter differs slightly for some shapes, the concept is always the same. For instance, the formula for the perimeter of a rectangle is P = 2l + 2w, while the formula for the perimeter of a triangle is P = a + b + c. Have your child put these formulas to practice using the problems below.

1. The sides of a square are 15 cm long. What is its perimeter?

Because all sides of a square are the same length, the perimeter can be calculated by adding the length of one side four times or by multiplying the length of the side by four. The equation should look like this: P = 15 + 15 + 15 + 15 = 60 or P = 4(15) = 60. The answer is 60 cm.

2. The base of a triangle is 5 inches, and its two sides are 4 inches long. Find the perimeter.

The perimeter here is calculated by adding the sides together: P = 5 + 4 + 4 = 13 inches.

### Area

The formula for calculating the area (A) of rectangles and parallelograms is A = lw, also written as A = bh. The area for a triangle can be found by calculating A = ½bh. Remind your child to label the answers using square units.

1.Find the area of a rectangle that's two inches long and five inches wide.

For this problem, A = 2 x 5 = 10 square inches.

2. A triangle has a base of four feet and a height of ten feet. Find the area.

The formula should look like this: A = ½(4)(10). Your child should begin by multiplying four by ten, which equals 40. Then, he or she should take half of 40, which is 20. The area of this triangle is 20 square feet.

### Volume

The formula used to calculate the volume of rectangular prisms is V = lwh. Another way to think of this formula is multiplying the height of the shape by the area of its base. Remember that all answers relating to volume should be labeled using cubic units.

1. A cube has a height of ten centimeters. What is its volume?

Because all the sides of a cube area the same, the length and width of this cube are also ten centimeters. Using the formula, plug in the numbers like this: V = 10 x 10 x 10. The answer is 1,000 cubic centimeters.

2. The area of a rectangular prism's base is 42 square feet. Its height is three feet. What is its volume?

Remember that another way to find volume is multiplying the area of the base by the height. In this case, all we need to do is multiply 42 (the area of the base) by the height: 42 x 3 = 126. The answer is 126 cubic feet.
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