11.2 areas of triangles, trapezoids, and rhombi. objectives find areas of triangles find areas of...

11.2 Areas of Triangles, Trapezoids, and Rhombi

Objectives

• Find areas of triangles

• Find areas of trapezoids

• Find areas of rhombi

Area of Triangles

• If the triangle has the area of A square units, a base of b units, and a height of h units, then…

A=1/2bh

A

B

C

b

h

Example 1:

Find the area of the triangle if the base is 9 in. and the height is 5 in.

A=1/2bh

B

A

C

9

5

Example 1:

Since the base is 9 in. and the height is 5 in. your equation should read,

A=1/2(5x9) Solve

A=1/2(45) Multiply.

A=22.5 Multiply by ½.

The area of triangle ABC is 22.5 square inches.

Area of Quadrilaterals Using Δ's

The area of a quadrilateral is equal to the sum of the areas of triangle FGI and triangle GHI.

A (FGHI)= ½(bh) + ½(bh)

F

g

G

I H

Example 2:

Find the area of the quadrilateral if FH= 37 in.

18 in.

9 in.

F

G

I H

Example 2:

A= ½(37x9)+ ½(37x18) Solve.

A= ½(333) + ½(666) Multiply.

A= 166.5 + 333 Add.

A= 499.5 square inches

Area of a Trapezoid

If a trapezoid has an area of A units, bases of b1 units and b2 units and a height of h units, then…

A= ½ h (b1+b2)h

b2

b1

Example 3:

Find the area of the trapezoid.

12 yd.

16 yd.

24 yd.

14 yd.

Example 3:

A= ½x12(16+24) Add.

A= ½x12(40) Multiply.

A= ½(480) Multiply.

A= 240 square yards.

Example 4:Area of a trapezoid

on the coordinate plane.

Since TV and ZW are horizontal, find their length by subtracting the x-coordinates from their endpoints.

T V

Z W

(-3,4) (3,4)

(-5,-1) (6,-1)

Example 4:

TV= |-3-3|TV= |-6|TV= 6

ZW= |-5-6|ZW= |-11|ZW= 11

Because the bases are horizontal segments, the distance between them can be measured on a vertical line. That is, subtract the y-coordinates.

H= |4-(-1)| H= |5|H= 5

Example 4:Now that you have the height and bases, you can

solve for the area.

A= ½h(b1+ b2)

A= ½(5)(6+11) Substitution.

A= ½(5)(17) Addition.

A= ½(85) Multiply.

A= 42.5 square units.

Area of Rhombi

If a rhombus has an area of A square units and diagonals of d1 and d2 units, then…

A= ½(d1xd2)

(AC is d1, BD is d2)

A

B

D

C

d1d2

Example 5:

Find the area of the rhombus if ML= 20m and NP= 24m.

M

L

N

P

Example 5:

A= ½(20x24) Multiply.

A= ½(480) Multiply.

A= 240 Square meters.

Rhombus on Coordinate Plane

To find the area of a rhombus on the coordinate plane, you must know the diagonals.

To find the diagonals...subtract the x-coordinates to find d1, and subtract

the y-coordinates to find d2.

Example 6:

Find the area of a rhombus with the points E(-1,3), F(2,7), G(5,3), and H(2,-1) F (2,7)

G (5,3)

H (2,-1)

E (-1,3)

Let EG be d1 and FH be d2

Subtract the x-coordinates of E and G to find d1

d1= |-1-5|d1= |-6|d1= 6

Subtract the y-coordinates of F and H to find d2

d2= |7-(-1)|d2= |8|d2= 8

F (2,7)

G (5,3)

H (2, -1)

E (-1,3)

d1

d2

Now that you have D1 and D2, solve.

A= ½(d1xd2)

A= ½(6x8) Multiply.

A= ½(48) Multiply.

A= 24 sq. units.

Find the Missing Measures

Rhombus WXYZ has an area of 100 square meters. Find XZ if WY= 20 meters. X

Y

Z

W

Use the formula for the area of a rhombus and solve for D1 (XZ)

A= ½(d1xd2)

100= ½(d1)(20) Substitution.

100= 10(d1) Multiply.

10=d1 Divide.

XZ= 10 meters

Postulate 11.1

Postulate 11.1: Congruent figures have equal areas.

Assignment:

• Pre-APPg. 606 #13-21, 22-28 evens,

30-35

• GeometryPg. 606 #13 – 21, 30 - 35