Mathematics Grade 7 15 min

Find the area or missing side length of a rectangle

Find the area or missing side length of a rectangle

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Introduction & Learning Objectives

Learning Objectives Define and identify the length and width of a rectangle. Accurately calculate the area of a rectangle using the formula A = l × w. Determine a missing side length of a rectangle when given its area and the other side length. Apply appropriate square units when expressing the area of a rectangle. Solve word problems that require finding the area or a missing side length of a rectangle. Use inverse operations (division) to find a missing side length from a given area. Ever wondered how much paint you'd need to cover a wall, or how much carpet for your room? 🏠 It all starts with understanding rectangles! In this lesson, you'll learn how to calculate the space inside a rectangle, called its area, and how to find a side length if you know the area...
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Key Concepts & Vocabulary

TermDefinitionExample RectangleA four-sided polygon with four right angles, where opposite sides are equal in length.A standard sheet of paper, a door, a football field. Length (l)The longer side of a rectangle, or one of the two distinct dimensions.If a rectangle is 10 cm by 5 cm, the length is 10 cm. Width (w)The shorter side of a rectangle, or the other of the two distinct dimensions, perpendicular to the length.If a rectangle is 10 cm by 5 cm, the width is 5 cm. Area (A)The amount of two-dimensional space a shape covers, measured in square units.A rectangle that is 3 cm long and 2 cm wide has an area of 6 square centimeters (6 cm²). Square UnitA unit of measurement for area, representing a square with sides of one unit length (e.g., square centimeters, square meters).cm², m², ft². For...
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Core Formulas

Area of a Rectangle $A = l \times w$ Use this formula to calculate the total two-dimensional space covered by a rectangle, where $A$ is area, $l$ is length, and $w$ is width. Finding Missing Length (given Area and Width) $l = A / w$ Use this formula to find the length of a rectangle when you know its area ($A$) and its width ($w$). This is derived from the area formula. Finding Missing Width (given Area and Length) $w = A / l$ Use this formula to find the width of a rectangle when you know its area ($A$) and its length ($l$). This is also derived from the area formula.

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Sample Practice Questions

Challenging
The perimeter of a rectangle is 30 cm. The length is 3 cm longer than the width. What is the area of the rectangle?
A.30 cm²
B.54 cm²
C.63 cm²
D.150 cm²
Challenging
The side lengths of a rectangle are in the ratio 5:2. If the area of the rectangle is 90 square meters, what is the length of the longer side?
A.9 m
B.10 m
C.15 m
D.18 m
Challenging
A square has an area of 64 cm². The square is reshaped into a rectangle with the same area. If the new rectangle has a width of 4 cm, what is its length?
A.8 cm
B.12 cm
C.16 cm
D.20 cm

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