Areas of Quadrilaterals

Areas of Quadrilaterals

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

Multiple Choice

What is the length of a diagonal of a square that has an area of 36 square centimeters?

• 6 cm

• $6\sqrt{2}$ cm

• $6\sqrt{3}$ cm

• 18 cm

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 perpendicular distances. The height is the distance between the parallel lines. The “base” is the average of the two bases, which is also the length of the midsegment.

Multiple Choice

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

• 130 cm²

• 140 cm²

• 180 cm²

• 260 cm²

Rhombus and Kite

A kite can be broken down into a pair of isosceles triangles. A rhombus is four right triangles. In both cases, the area can be expressed as one-half the product of the diagonals.

Multiple Choice

What is the area of the figure shown?

• 30 cm²

• 60 cm²

• 65 cm²

• 120 cm²

Distance Between Two Geometric Objects

In general, the distance between two objects is measured perpendicularly. For example, the distance between parallel lines is the is measured at right angles to both lines, like the height of a trapezoid.

Multiple Choice

What is the distance between the lines

 $y=\frac{1}{2}x$  and  $y=\frac{1}{2}x+5$  ?

• 5 units

•  $\sqrt{5}$  units

•  $2\sqrt{5}$  units

•  $4\sqrt{5}$  units

Multiple Choice

The distance from the center of a regular polygon to one its sides is called ___________.

• an apothem

• a diagonal

• a radius

• a side

Poll

Are you ready to calculate some area?

• Yes

• No

• What's area again?