Geometry Word Problems and Solutions

Geometry word problems often involve formulas for calculating perimeter, area or volume of 2- and 3-dimensional shapes. Help your child practice at home by creating your own word problems or using opportunities in real life. For sample word problems and explanations, read on.

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How Can I Write My Own Geometry Word Problems?

To write your own word problems, think about real-world situations that use geometry. Plan word problems that deal with the area or perimeter of rooms or the volume of 3-dimensional spaces like swimming pools. Make sure you provide your child with the necessary formulas. Most elementary students are not required to memorize these equations.

Finally, take advantage of real-world situations. For example, if you're redecorating a room, you can have your child calculate the perimeter to determine how much paint you'll need to buy. Remember that such situations will help your child see connections between school and the real world, which can make schoolwork seem more significant.

Geometry Word Problems

1. Kelly wants to put new carpet in her bedroom, which is ten feet long and 12 feet wide. If carpet costs $5 per square foot, how much will she spend on carpet?

This problem requires two steps. Begin by finding the area of the room using this equation: Area = length x width = 10 feet x 12 feet = 120 square feet. Then, multiply 120 by 5 to find out how much the carpet will cost. Kelly will have to spend $600.

2. Your dad places a 10-foot ladder against the wall. The bottom of the ladder is five feet from the wall. How many feet up the wall does the ladder reach?

For this problem, your child will have to use the Pythagorean theorem, which is a^2 + b^2 = c^2. Have your child begin by drawing lines to represent the ground, the wall and the ladder. This will form a right triangle. Then, label the sides of the triangle to represent the parts of the equation: the ground is a^2, the wall is b^2, and the ladder is c^2.
Next, plug in the known numbers. The equation should look like this: 5^2 + b^2 = 10^2. Square the known numbers - 25 + b^2 = 100 - which should allow your child to figure out that b^2 = 75. Finally, determine the square root of 75. The answer is the ladder reaches approximately 8.66 feet up the wall.

3. What's the capacity of a swimming pool that is 60 feet long, 20 feet wide and six feet deep?

Volume is used for 3-dimensional shapes. For rectangles, the formula is volume = length x width x height. Plug-in the numbers so that the formula looks like this: V = 60 x 20 x 6 = 7,200 cubic feet.
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