Mathematics Grade 7 15 min

Area of rectangles and parallelograms

Area of rectangles and parallelograms

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1

Introduction & Learning Objectives

Learning Objectives Define area and identify its standard units. Accurately calculate the area of any given rectangle using the formula A = length × width. Accurately calculate the area of any given parallelogram using the formula A = base × height. Identify the base and perpendicular height of a parallelogram. Solve real-world problems involving the area of rectangles and parallelograms. Explain the relationship between the area formula for rectangles and parallelograms. Ever wondered how much paint you need for a wall or how much carpet for a room? 🤔 It all comes down to understanding 'area'! In this lesson, you'll discover how to measure the space inside flat shapes, specifically rectangles and parallelograms. Learning about area is a fundamental skill th...
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Key Concepts & Vocabulary

TermDefinitionExample AreaThe amount of two-dimensional space a flat surface or shape covers, measured in square units.If a square has sides of 1 cm, its area is 1 square centimeter (1 cm²). RectangleA quadrilateral (a four-sided polygon) with four right (90-degree) angles. Opposite sides are equal in length and parallel.A typical door, a sheet of paper, or a football field are all rectangular shapes. ParallelogramA quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal.A tilted rectangle, or a rhombus (which is a special type of parallelogram). Base (of a parallelogram)Any one of the sides of a parallelogram that is chosen to be the 'bottom' side for area calculation. It's often the side the parallelogram appears t...
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Core Formulas

Area of a Rectangle $$A = l \times w$$ To find the area (A) of a rectangle, multiply its length (l) by its width (w). This formula works because a rectangle can be thought of as rows of square units. Area of a Parallelogram $$A = b \times h$$ To find the area (A) of a parallelogram, multiply the length of its base (b) by its perpendicular height (h). This formula is derived from cutting a triangular section from one end and moving it to the other to form a rectangle.

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Sample Practice Questions

Challenging
A rectangular piece of paper is 20 cm long and 15 cm wide. A parallelogram with a base of 8 cm and a height of 5 cm is cut out from the center of the paper. What is the area of the remaining paper?
A.300 cm²
B.260 cm²
C.40 cm²
D.220 cm²
Challenging
The base of a parallelogram is increased by 20% and its perpendicular height is decreased by 10%. What is the resulting percentage change in the area of the parallelogram?
A.It increases by 10%
B.It decreases by 2%
C.It increases by 8%
D.It does not change.
Challenging
Two parallelograms, P1 and P2, have the same area. P1 has a base of 16 cm and a height of 9 cm. If P2 has a base of 12 cm, what is its height?
A.12 cm
B.9 cm
C.16 cm
D.6.75 cm

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