Area: Triangles and Trapezoids

Lesson 10-2 p.509

1. Start the Bellwork Quiz.2. Have your HW, red pen, and

book on your desk.

Triangles When finding the area of triangles,

remember that a triangle is half of a parallelogram.

Triangles Now you can see why the formula for the

area of a triangle makes sense:

A = bh or A = bh 2

12

Triangles Let’s look at an example:

4 feet

5 feet A = bh = 4 (5) = 20 2 2 2

or 10 ft2

Try This Find the areas:

12 in.

3 ft.5 mi.

6 miles

7 miles

Try This Find the areas:

12 in.

3 ft.5 mi.

6 miles

7 miles

216 in2 or1.5 ft2

Try This Find the areas:

12 in.

3 ft.5 mi.

6 miles

7 miles

216 in2 or1.5 ft2 15 mi2

Trapezoids Trapezoids have different formula. It looks

like this:

A = h (b1 + b2) or A = h(b1 + b2)

2b1

b2

h

12

Trapezoids A = h (b1 + b2) or A = h(b1 + b2)

2Note that there are 2 bases—base 1 and

base 2. The formula takes the average of the two bases multiplied by the height.

b1

b2

h

12

Trapezoids Let’s try an example:

A = h (b1 + b2) A = 3.5 (4 + 6)

2 2A = 3.5 (5) = 17.5 ft2

4 ft

6 feet

3.5 ft

Try This Find the area:

24 mm

33 mm

12 mm

Try This Find the area:

24 mm

33 mm

12 mm 342 mm2

Try This Find the area:

4 feet2 feet

4.5 feet

Try This Find the area:

4 feet2 feet

4.5 feet13 ft2

Example Some shapes look unusual, but when you

remember just 3 formulas, you can calculate the area.

Which two shapes do yousee in the figure at the left?

Example There is a square (parallelogram) and a

triangle. To find the area, first find the area of the parallelogram and then add it to the area of the triangle.

Example

3 ft 2 ft

The square has an area of A = bh or 3 (3) or 9 ft2.The triangle has an area of A = ½ bh or ½ (3) (2) or 3 ft2.The total area if 9 + 3 or 12 ft2

Try This Find the area:

4 cm

6 cm

8 cm

6 cm

Try This Here is a hint:

4 cm

6 cm

8 cm

6 cm

Try This Here is a hint:

4 cm

6 cm

8 cm

6 cm

For the rectangle:A = bhA = 6 (4) = 24 cm2

For the trapezoid:A = ½ h (b1 + b2)A = ½ (2) (4 + 6)A = 10 cm2

Total area =24 + 10 = 34 cm2

Try This Is there another way to divide this up?

4 cm

6 cm

8 cm

6 cm

Try This How about like this:

4 cm

6 cm

8 cm

6 cm

Try This How about like this:

4 cm

6 cm

8 cm

6 cm

For the rectangle:A = bh = 8 (4) = 32 cm2

For the triangle:A = ½ bh = ½ (2) (2) = 2 cm2

The total area is 32 + 2 or34 cm2

Agenda

PA#38Pp.512-513 #8-

16 even, 17, 19

Please start Bellwork #

HW, red pen book on desk.

Agenda

PA#Workbook pp.83 & 84

Benchmark 3 is Friday.