Expand Linear Expressions Worksheets Grade 7

1. A rectangular playground is drawn on a coordinate grid with corners at (0, 0), (18, 0), (18, 12), and (0, 12). Charlotte wants to build a new rectangular sandbox that is attached to the right side of the playground. The sandbox has the same height as the playground and a width of 7 units. Using the distributive property, write an expression for the total area of the playground and sandbox combined, then calculate the total area.
2. Liam is designing a rectangular garden for his school project. The length of the garden is represented by (3x + 5) feet, and the width is (2x - 1) feet. He needs to calculate the total area of the garden to determine how much soil to buy. What is the expanded expression, in square feet, that represents the area of Liam's garden?
3. Olivia is designing a rectangular garden on a coordinate grid. The garden has corners at (0, 0), (17, 0), (17, 9), and (0, 9). She decides to divide the garden into two rectangular sections by adding a fence parallel to the left and right sides, located 7 units from the left edge. Using the distributive property, write an expression for the total area of the garden and then calculate the total area.

…and 4 more problems

1. 5(10x - 15) + 3(20 - 5x) = ?
2. A rectangular community garden plot has a length that is 5 meters more than three times its width. The gardeners want to expand the plot by adding a uniform pathway around all sides that increases both dimensions by 4 meters. If the original width is w meters, write a simplified expression for the total area of the expanded garden plot including the pathway.
3. Aroha is designing a rectangular community garden. The length of the garden is 14 meters more than 9 times its width. To make it wheelchair accessible, a uniform concrete path of 3 meters wide will be added around the entire garden. If the original width of the garden is represented by w meters, write a simplified expression in expanded form for the total area of the garden including the concrete path.

…and 4 more problems

1. A rectangular community garden is drawn on a coordinate grid with corners at (0, 0), (25, 0), (25, 15), and (0, 15). The garden is divided into two rectangular sections by a vertical fence. The left section has a width of 10 units, and the right section has a width of 15 units. Using the distributive property, write an expanded expression for the total area of the garden, and then calculate the total area.
2. A rectangular community center is drawn on a coordinate grid. The base of the building has corners at (0, 0), (30, 0), (30, 20), and (0, 20). Liam wants to add a rectangular annex to the right side of the building. The annex has the same height as the original building and a width of 15 units. Write an expanded expression using the distributive property for the total area of the building and annex combined, then calculate that total area.
3. Mason is building a rectangular treehouse platform. The platform's length is 12 feet more than twice its width. He decides to add a safety railing that extends 3 feet beyond the platform on all sides. If the original width of the platform is w feet, write a simplified expression in expanded form for the total area of the platform plus the railing extension.

…and 3 more problems