Area of a Trapezoid

October 3rd PLC

Trapezoid

• A trapezoid is a quadrilateral with exactly one pair of parallel sides.

• In the United Kingdom, this shape is called a trapezium.

The formula for the area of a trapezoid is 1/2 the

sum of the two bases times the height.

Let's try it!

The bases of this trapezoid are 6 units and 10 units. The height of this trapezoid is 7 units.

A = 1/2 (6 + 10)(7)

A = 1/2 (16)(7)

A = (8)(7)

A =56

So, the area of the trapezoid is 56 square units.

​Pro Tip!

​Remember hat a formula is not scary! The letters are placeholders.
A=½ (_X_)_

​b₁

​b₂

​h

Multiple Choice

What name do we use to label the 2 sides that are parallel?

• Bases

• Heights

• Altitudes

• Widths

• Lengths

Multiple Select

What properties do ALL trapezoids have?

• 1 pair of Parallel Sides

• Right Angles

• 4 Sides

• Opposite Congruent Sides

Multiple Select

Which two measurements can be used as the base 1 and base 2 for this trapezoid?

• 4m

• 5m

• 8m

Multiple Choice

What is the height of this trapezoid?

• 4m

• 5m

• 8m

Multiple Choice

What is the area of this trapezoid?

• $$80m^2$$

• $$32.5m^2$$

• $$26m^2$$

• $$50m^2$$

Multiple Choice

What name do we use to label the distance between the two bases?

• Length

• Height

• Base

• Width

Multiple Choice

Fill in the area formula for the green trapezoid.

$$A=\frac{1}{2}\cdot h\cdot\left(b_1+b_2\right)$$  

• $$A=\frac{1}{2}\cdot6\cdot\left(5+9\right)$$  

• $$A=\frac{1}{2}\cdot5\cdot\left(6+9\right)$$  

• $$A=\frac{1}{2}\cdot9\cdot\left(5+6\right)$$  

Multiple Choice

Shown is the correct formula for the green trapezoid. Which shows the next correct step?
$$A=\frac{1}{2}\cdot6\cdot\left(5+9\right)$$  

• $$A=\frac{1}{2}\cdot6\cdot14$$  

• $$A=\frac{1}{2}\cdot30+9$$  

• $$A=\frac{1}{2}\cdot6\cdot45$$  

Multiple Choice

Shown is the correct next step in calculating the area. So what should the area be?

$$A=\frac{1}{2}\cdot6\cdot14$$  

• 42

• 10

• 84

• 17

Multiple Select

Our answer was missing units! What should the area units be? (There are TWO correct answers!)

• ft

• ft²

• units

• sq ft

Multiple Choice

Fill in the area formula for the red trapezoid.

$$A=\frac{1}{2}\cdot h\cdot\left(b_1+b_2\right)$$  

• $$A=\frac{1}{2}\cdot5\cdot\left(4+8\right)$$

• $$A=\frac{1}{2}\cdot4\cdot\left(5+8\right)$$

• $$A=\frac{1}{2}\cdot8\cdot\left(4+5\right)$$

Multiple Choice

Shown is the correct formula. What's next?

$$A=\frac{1}{2}\cdot5\cdot\left(4+8\right)$$  

• $$A=\frac{1}{2}\cdot5\cdot12$$  

• $$A=\frac{1}{2}\cdot20\cdot40$$  

• $$A=\frac{1}{2}\cdot5\cdot32$$  

Multiple Choice

Shown is the correct next step. What is the area of the red trapezoid?

$$A=\frac{1}{2}\cdot5\cdot12$$  

• 30 sq mm

• 11 sq mm

• 70 sq mm

• 140 sq mm

Multiple Choice

Find the area

• 126

• 252

• 350

• 175

Remember:

follow these 3 steps...

​Step 1:

​Add the bases.

Some text here about the topic of discussion

​Step 2:

​Step 3:

Multiply the sum by the height.

Divide the product by 2.​