Lesson on Area

Areas of Quadrilaterals

We can think of the area of a two-dimensional ("plane") object as the number of square units it contains.

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Each of the figures to the right has the same area.

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You can see that counting boxes sometimes works well and sometimes not.​

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Fortunately, there are formulas so we don't have to count boxes!

YOU DO NOT HAVE TO MEMORIZE THESE! YOU WILL BE GIVEN A FORMULA SHEET ON THE SOL!

Area

Area is a measure of two-dimensional space.  Area is measured in square units, such as square feet or cm². The two dimensions of a square unit must be perpendicular.

Rectangles & Parallelograms (& Squares)

The area of rectangles, parallelograms, and squares are all effectively the same. The important component is that the two dimensions measured are perpendicular.

Multiple Choice

What is the area of a rectangle that measures 18 inches by one foot.

• 18 square inches

• 18 square feet

• 216 square inches

• 216 square feet

Multiple Choice

What is the area of the parallelogram shown?

• 30 cm²

• 35 cm²

• 40 cm²

• 50 cm²

Triangles

A triangle can always be drawn as half of a rectangle or parallelogram. Any altitude of a triangle can be used as the height when paired with the corresponding base.

Multiple Choice

What is the area of the shaded triangle?

• 16 cm²

• 20 cm²

• 24 cm²

• 32 cm²

Trapezoids

The area of a trapezoid is also calculated by multiplying the hight by the sum of the bases. The height is the distance between the parallel lines. The “base” refers to 2 bases - the top and bottom.

Remember to add the bases, multiply that by height, then divide by 2!

Multiple Choice

What is the area of the trapezoid shown in the diagram?

• 130 cm²

• 140 cm²

• 180 cm²

• 260 cm²

Remember to use a calculator!

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Let's practice some more.

Multiple Choice

Determine the area of the parallelogram:

• 166.41 sq. in

• 91.59 sq. in.

• 45.8 sq. in.

• 1181.51 sq. in.

Multiple Choice

Find the area of the triangle.

• 27.3 mi²

• 27 mi²

• 54 mi²

• 54.6 mi²

Multiple Choice

Find the area of the parallelogram.

• 135 mm²

• 130 mm²

• 270 mm²

• 275 mm²

Multiple Choice

Find the area.

• 300 m²

• 40 m²

• 80 m²

• 150 m²

Multiple Choice

Find the area of the triangle.

• 80 yd²

• 40 yd²

• 100 yd²

• 18 yd²

Multiple Choice

Find the area.

• 35 square units

• 30 square units

• 70 square units

• 168 square units

Multiple Choice

Find the area.

• 41.5 in²

• 21.5 in²

• 430 in²

• 1.5 in²

Multiple Choice

Find the area.

• 16 yd²

• 42 yd²

• 22 yd²

• 28 yd²

Multiple Choice

PERIMETER PRACTICE! What is the perimeter?

• 20

• 40

• 60

Multiple Choice

Find the area of this composite shape.

• 60 ft²

• 108 ft²

• 168 ft²

• 154 ft²

Multiple Choice

PERIMETER PRACTICE! What is the perimeter?

• 20

• 5

• 4