Bell Work:

Simplify

√50

Answer:

5√2

LESSON 75:AREA OF A TRAPEZOID

Recall that we multiply the base and height of a parallelogram to find its area. The base and height are perpendicular.

Also recall that the product of multiplying the base and height of a parallelogram is the area of a rectangle.

If the parallelogram is not a rectangle, its area is nevertheless equal to the area of a rectangle with the same base and height.

This is so because the portion of the parallelogram outside the rectangle matches the “hole” inside the rectangle.

To find the area of a trapezoid we can find the area of a rectangle with the equivalent area.

A trapezoid has two bases, which are the parallel sides.

The perpendicular distance between the bases is the height.

If we multiply either one of the bases by the height the result is a rectangle that is either too small or too large.

Instead of multiplying one of the bases by the height, we multiply the average length of the bases by the height.

The average length of the bases is the length halfway between the length of the shorter base and the length of the longer base.

Formula for finding the area of a trapezoid:

Area = average length of bases x height

A= ½(b + b )h1 2

Example:

Erik needs to replace the shingles on the south side of his roof. The section of roof is a trapezoid with the dimensions shown. How many square feet of shingles does he need to cover this section of the roof? 8 feet

12 feet

24 feet

Answer:

Average length of bases

= 8 ft + 24 ft = 16 feet

2

16ft x 12ft

= 192 feet squared

Example:

The bases of a trapezoid are 12cm and 18cm. The height of the trapezoid is 8cm. Find the area of the trapezoid.

Answer:

A = ½(12cm + 18cm)8cm

A = ½(30cm)8cm

A = 15cm(8cm)

A = 120 cm squared

Example:

Find the area of the trapezoid.10 cm

10 cm

8 cm

16 cm

Answer:

104 cm squared

HW: Lesson 75 #1-25