11-511-5Area of Triangles and TrapezoidsArea of Triangles and Trapezoids

Pages 489-492

Indicator(s)-

M6 Use strategies to develop formulas for finding area of trapezoids

P8 Use formulas in problem solving

Area of TrianglesArea of Triangles A=A=½bh½bh• A triangle is a three-sided polygon.

• The area of a triangle can be defined by half of the product of the length of its base and its height. The height is always perpendicular to the base, exactly like the base and height of a

parallelogram.

• A=½bh

ExampleExample

• Find the area of the triangle below. Round to the nearest tenth if necessary.

• A=½bh

• A=½(9)(3.2)

• A=½(28.8)

• A= 14.4 cm2

• The area of the given triangle is 14.4 cm2

9 cm.

3.2 cm

Area of Trapezoids Area of Trapezoids A=A=½h(b½h(b11+b+b22))

• A trapezoid has two (2) bases, b1& b2. The height of the trapezoid is the perpendicular distance between the two bases.

• A=½h(b1+b2)

b1

b2

h

ExampleExample

• Find the area of the trapezoid below. Round to the nearest tenth if necessary.

• A=½h(b1+b2)

• A=½(3)(4 + 7.6)

• A=½(3)(11.6)

• A= 17.4 m2

• The area of the given trapezoid is 17.4 cm2

4 m

3 m

7.6 m

ExampleExample• The shape of the state of Montana resembles

a trapezoid. Estimate its area in square miles.

• A=½h(b1+b2)

• A=½(285)(542 + 479)

• A=½(285)(1021)

• A≈ 145,493 mi2

• The area of the Montana is about 145,493 mi2.

542 mi

285 mi

479 mi

What if… What if… you are dealing with two different measurements?

Find the area of the given triangle. Round to the nearest tenth if necessary.

• A=½bh• A=½(13 in)(1 ft)• CONVERT & SOLVE! • A=½(13 in)(12 in)• A= 78 in2

13 in

1 ft

Challenge…Challenge…

• Find the area of the trapezoid shown. Round to the nearest tenth if necessary.

• A=½h(b1+b2)

• HINT: HINT: To find the height, you will have to use the Pythagorean Theorem.To find the height, you will have to use the Pythagorean Theorem.

10 cm

6 cm

9cm