how to solve area and perimeter word problems

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Word Problems: Area and Perimeter of a Rectangle

A rectangle is a parallelogram with four right angles. All rectangles are also parallelograms, but not all parallelograms are rectangles.

The perimeter P of a rectangle is given by the formula, P = 2 l + 2 w , where l is the length and w is the width of the rectangle.

The area A of a rectangle is given by the formula, A = l w , where l is the length and w is the width.

You will often encounter word problems where two of the values in one of these formulas are given, and you are required to find the third.

The perimeter of a rectangular pool is 56 meters. If the length of the pool is 16 meters, then find its width.

Here the perimeter and the length of the rectangular pool are given. We have to find the width of the pool.

Given that, the perimeter is 56 meters and the length is 16 meters. So, substitute these values into the formula.

56 = 2 ( 16 ) + 2 w

56 = 32 + 2 w

Subtract 32 from both sides.

Divide each side by 2 .

Therefore, the width of the rectangular pool is 12 meters.

The area of a rectangular fence is 500 square feet. If the width of the fence is 20 feet, then find its length.

Here the area and the width of the rectangular fence are given. We have to find the length of the fence.

Given that, the area is 500 square feet and the width is 20 feet. So, substitute these values into the formula.

500 = l × 20

Divide each side by 20 to isolate l .

Therefore, the length of the rectangular fence is 25 feet.

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Area and Perimeter Word Problems Worksheets

These worksheets and lessons help students learn how to tackle word problems that involve finding area and perimeter. What is the difference between Area and Perimeter? When you learn areas and perimeters, you end up pulling your hair; because they both look like the same thing but really are two completely different things. Now, we will list down the differences between the area and the perimeter of a shape. Perimeter is the total distance which is covered around any shape. For example, the length of the fence around a football court is called the perimeter. It is calculated by adding each side’s fencing length. The area is the space covered by the shape within a perimeter. The area is space of land, which the football court is covering. To understand areas and perimeter, let’s play a game. Lets apply this to a local park, the park is a big rectangle. You have to determine its perimeter and area. - Since it is a rectangle, you know that the opposite sides are off the equal length, so, there are two sides of length 150 m and two sides of length 400 m. - For calculating the perimeter, you can just add all the sides together. 400 + 400 + 150 + 150 = 1100 m. The unit will be the same as the unit of length given. - The area of a rectangle is calculated by multiplying length and breadth. So, we have to take only one side of each type. 150 x 400 = 60,000 square meter. The unit is square meter because it covers space taken both by length and breadth.

Aligned Standard: Grade 4 Measurement - 4.MD.3

• Oscar's Drawing Room Step-by-Step Lesson - How big is this pup's room? You work it out.
• Guided Lesson - You will find cost incorporated in these problems as we start to look for new approaches toward algebra.
• Guided Lesson Explanation - I take a concise approach on these problems. I usually just slap the units on at the end, but I tried my best to keep them in throughout.
• Practice Worksheet - Who would have know that 2 sentence problems could require a page to answer?
• Perimeter and Area of Polygons Five-Worksheet Pack - Show us your mastery of polygons.
• Matching Worksheet - Again, I purposely left the units off the answers to make it more challenging.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

This skill is used so much in the construction of just about every physical product ever made.

• Homework 1 - Adler purchases a new house, but the main gate of house looks ugly because of color. He measures the gate 8 feet by 10 feet. He wants to paint the main gate with white color at a cost of $20 per square foot. How much will it cost for Adler to add color to his main gate?
• Homework 2 - Byron and Cari are best friends. Byron wants to give a collage photo frame to Cari on her birthday. He measures the photo frame at 12 inches by 18 inches. He wants to cover the photo frame with a golden cloth at a cost of $7 per square inch. How much will it cost for Byron to cover his photo frame?
• Homework 3 - Alice already has a TV, but it is black and white. She wants to buy a new color LCD TV. She went to the market and found an LCD TV which measures 20 inches by 26 inches.

Practice Worksheets

I love to give projects on this type of thing. I always have students do real world tasks like determining how many cars can park in a lot.

• Practice 1 - Alex has rectangular cookies. The length of each cookie is 6 cm and the width is 4 cm. Find the area of the cookies.
• Practice 2 - What is the height of a rectangular stone with a perimeter of 260.2 mm and a base length of 75.4 mm?
• Practice 3 - Luca has a keyboard. The length of the keyboard is 18 inches and the width is 10 inches. Find the area of the keyboard.

Math Skill Quizzes

A few of these problems will require some reading stamina on your part.

• Quiz 1 - Gerund is a carpenter. He made a square table. He wants to put a copper sheet on the table at a cost of $42 per square inch. He knows that the perimeter of the table is 120 inches. Calculate the cost of the copper sheet.
• Quiz 2 - Greeley is a name plate designer. He designed a nameplate that was 10 inches by 15 inches. The cost to design these quality plates is $13 per square inch. What was the total cost of the nameplate?
• Quiz 3 - Marshal wants to paint the front wall of his house. He measures the front wall at 12 feet by 13 feet. The cost of paint will be $13 per square foot. What is the total cost of the paint?

A Problem Worked Out For You

Example Problem: Tanya is a builder that specializes in installing ceramic tile. She gets a job to replace the tile floors at the local Town Hall. The floor that she is focused on replacing is 32 feet by 54 feet. The particular tile that the Town chose to use costs $12 per square foot. How much will it cost for Tanya to buy enough tile to complete the job?

Solution: The cost of the tile is $12 per square foot. If we determine the total square footage, we would multiply those two together to find the solution (total area x cost per square foot = cost). To determine the total area, we would multiply the length and width of the area (l x w = square footage). To do the math 32 x 54 = 1,728 square foot. We now have everything that we need to solve this (total area x cost per square foot = cost) or (1,728 square foot x $12 per square foot = $20,736). That is quite a bit of tile.

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Area and Perimeter - Problem Sums

1. adriel ran 5 rounds of a square ground of side 70 m. find the total distance he ran..

2. Mrs. Rao gives one rectangular card of sides 18 cm by 14 cm to each of her 7 pupils. She wants her pupils to glue a ribbon around the border of their own card. Find the length of the ribbon they will need altogether.

3. Lila has 9 square stamps of side 3 cm each. She glues them onto an envelope to form a bigger square. What area of the envelope does the bigger square cover?

4. Mrs. Bell cuts a 25 cm by 6 cm cloth into 5 equal pieces. What is the area of each piece?

5. You have 4 squares each of side 8 cm. Join the squares to form a bigger four-sided figure. What is the longest possible perimeter that you can get?