Simple Geometry Problems for Struggling Students

Solving Geometry Problems

Perimeter

Perimeter is the distance around the outside of an object, and it's calculated by adding together the lengths of all of the sides. Imagine that you're asked to find the perimeter of a rectangular garden that's 12 feet long and eight feet wide. This means there are two sides that are 12 feet long and two sides that are eight feet long. Here's how to calculate the perimeter:

P = 2L x 2W

= 2(12) + 2(8)

= 24 + 16

= 40 feet

Circumference

Circumference is the perimeter of a circle. The formula to find it is C = 2(pi)r, where 'pi' equals 3.14 and 'r' is the radius of the circle (r = 1/2 diameter). For example, let's say you're finding the circumference of a circle with a radius of five meters. Here are the calculations you would use:

C = 2(pi)r

= 2(3.14)(5)

= 6.28(5)

= 31.4 meters

Area

A shape's area is the amount of space it covers. For rectangles, you'll find the area by multiplying length by width. For instance, if you're asked to find the area of a room that's 11 meters long and seven meters wide, you'd multiply 11 x 7 to get the area of 77 square meters.

For circles, area is found using this formula: A = pi(r)^2. The 'r^2' tells you to multiply the circle's radius by itself. Let's say your teacher asks you to find the area of a pizza with a radius of eight inches. Here's how to solve this problem:

A = pi(r)^2

= 3.14 x 8 x 8

= 3.14 x 64

= 200.96 square inches

Volume

When you need to figure out how much space a 3-dimensional object takes up, or how much capacity it has, you'll use the volume formula. For rectangles, it's V = length x width x height, and for cubes, it's just V = s^3.

Imagine you're asked to find the volume of a cube-shaped box that's six inches tall. Since it's a cube, you know that the length and width of the box also equal six inches, so you'll find the answer by solving V = 6^3 = 6 x 6 x 6. The box's volume is 216 cubic inches.

For a cylinder, the formula for volume is V = (area of the base) x (height). Since the base of a cylinder is circular, you'll calculate its area using the formula for the area of a circle, A = pi(r)^2. Then you'll multiply this result by the cylinder's height. For instance, the volume of a cylindrical package with a radius of two centimeters and a height of nine centimeters would be found like this:

V = pi * r^2 * h

= 3.14 * 2^2 * 9

= 3.14 * 4 * 9

= 3.14 * 36

= 113.04 cubic centimeters