Area of Parallelograms

Student Summary

Any pair of a base and a corresponding height can help us find the area of a parallelogram, but some base-height pairs are more easily found than others.

When a parallelogram is drawn on a grid and has horizontal sides, we can use a horizontal side as the base. When it has vertical sides, we can use a vertical side as the base. The grid can help us find (or estimate) the lengths of the base and of the corresponding height.

Two parallelograms drawn on two grids.
Two parallelograms drawn on two grids. First parallelogram, 2 horizontal sides each 8 units long, 2 slanted sides that rise 2 vertical units over 4 horizontal units. Bottom horizontal side labeled, b. A 2-unit perpendicular segment labeled, h, connects the horizontal sides. Second parallelogram, 2 vertical sides each 6 units long, 2 slanted sides that rise 4 vertical units over 4 horizontal units. The left vertical side is labeled, b. A 4-unit perpendicular segment labeled, h, connects one vertex of the vertical side to a point on the other vertical side.

When a parallelogram is not drawn on a grid, we can still find its area if we know a base and a corresponding height.

A parallelogram with side lengths 10 units and 8 units. An 8-unit perpendicular segment connects one vertex of the 8 unit side to a point on the other 8 unit side.

In this parallelogram, the corresponding height for the side that is 10 units long is not given, but the height for the side that is 8 units long is given. This base-height pair can help us find the area.

Parallelograms that have the same base and the same height will have the same area; the product of the base and height will be equal. Here are 4 different parallelograms with the same pair of base-height measurements.

Four different parallelograms. Each parallelogram has a base labeled 3 and a height labeled 4.

Visual / Anchor Chart

Standards

Building On
3.OA.A

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Addressing
6.EE.2.c

Write, read, and evaluate expressions in which letters stand for numbers.

6.G.1

Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.