Learn on PengiBig Ideas Math, Course 1Chapter 4: Areas of Polygons

Lesson 1: Areas of Parallelograms

In Big Ideas Math Course 1, Grade 6 students learn how to derive and apply the area formula for a parallelogram using deductive reasoning, connecting it to the known area formula for a rectangle. The lesson covers the formula A = bh, where b is the base and h is the height, and students practice finding areas of parallelograms given whole numbers, fractions, and grid-based dimensions. A real-life application extends the concept to composite figures by subtracting the area of a cut-out shape from the total parallelogram area.

Section 1

Area of a Parallelogram

Property

A parallelogram can be rearranged into a rectangle with the same base and height. Choose any side of the parallelogram as the base (length bb), and let hh be the perpendicular distance between the base and the opposite side.
The area is given by the formula:

Area⁡=bh\operatorname{Area} = bh

Examples

  • A parallelogram has a base of 12 cm and a height of 5 cm. Its area is 12×5=6012 \times 5 = 60 square cm.
  • A section of a patio is shaped like a parallelogram with a base of 8 feet and a height of 6 feet. The area is 8×6=488 \times 6 = 48 square feet.
  • Even if the slanted side is 9 inches, if the base is 15 inches and the height is 7 inches, the area is 15×7=10515 \times 7 = 105 square inches.

Explanation

Think of a parallelogram as a slanted rectangle. By slicing off a triangle from one end and moving it to the other, you create a perfect rectangle. This new rectangle has the same base and height, which is why the area formula works!

Section 2

Area of Parallelograms on Coordinate Grids

Property

When a parallelogram is drawn on a coordinate plane with horizontal and vertical sides, we can use the coordinates to measure the base and height, then apply the parallelogram area formula.

Parallelogram Area: A=base×heightA = \text{base} \times \text{height}

Section 3

Using Area Formulas in Equations

Property

When solving problems involving area, you can use the area formula for a parallelogram to create equations. If the area of a parallelogram is AA and you know the base bb and height hh, then:

A=bhA = bh

To find an unknown dimension, use multiplication or division to solve the equation.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Area of a Parallelogram

Property

A parallelogram can be rearranged into a rectangle with the same base and height. Choose any side of the parallelogram as the base (length bb), and let hh be the perpendicular distance between the base and the opposite side.
The area is given by the formula:

Area⁡=bh\operatorname{Area} = bh

Examples

  • A parallelogram has a base of 12 cm and a height of 5 cm. Its area is 12×5=6012 \times 5 = 60 square cm.
  • A section of a patio is shaped like a parallelogram with a base of 8 feet and a height of 6 feet. The area is 8×6=488 \times 6 = 48 square feet.
  • Even if the slanted side is 9 inches, if the base is 15 inches and the height is 7 inches, the area is 15×7=10515 \times 7 = 105 square inches.

Explanation

Think of a parallelogram as a slanted rectangle. By slicing off a triangle from one end and moving it to the other, you create a perfect rectangle. This new rectangle has the same base and height, which is why the area formula works!

Section 2

Area of Parallelograms on Coordinate Grids

Property

When a parallelogram is drawn on a coordinate plane with horizontal and vertical sides, we can use the coordinates to measure the base and height, then apply the parallelogram area formula.

Parallelogram Area: A=base×heightA = \text{base} \times \text{height}

Section 3

Using Area Formulas in Equations

Property

When solving problems involving area, you can use the area formula for a parallelogram to create equations. If the area of a parallelogram is AA and you know the base bb and height hh, then:

A=bhA = bh

To find an unknown dimension, use multiplication or division to solve the equation.