how much paint do we need to paint all the rooms in our house?

How much paint do we need to paint all the rooms in our house?

bedroom

kitchen

TVroom

Square Area = s2 (s = side length)

Rectangle Area = lw (l = length and w = width)

Triangle Area = ½bh (b = base and h = height)

You can justify the area formula for triangles as follows:

The area of a triangle is half the area of a parallelogram with the same base and

height.

Area of a Parallelogram = bh

Area of a Triangle = ½bh

Be careful when identifying the height of a triangle! The height is NEVER a side of a

triangle unless the triangle is RIGHT.

h h

h

Ex 1: Find the area of..

a. A square whose sides have length 8 cm.

8 cm

8 cm

8 cm8 cmA = s2

A = 82

A = 64 cm2

b. A rectangle whose length is 5 m and width is 11 m.

5 m

11 m

A = lwA = (5)(11)A = 55 m211 m

5 m

c. A triangle whose side lengths are 3 in, 4 in, and 5 in.

A = ½ (4)(3)A = ½ (12)A = 6 in2

3 in

4 in5 in

Ex 2: Find the indicated side length.

a. A square with area 256 in2.

16 inA = s2 256 = s2 16 = s

16 in 16 in

16 in

b. A rectangle with area 345 ft and length 15 ft.

15 ft

23 ft

A = lw345 = 15w23 ft = w23 ft

15 ft

c. A triangle with area 12 mm and a base length of 6 mm.

A = ½ bh12 = ½ (6)h12 = 3h4 mm = h

6 mm

4 mm

Parallelogram Area = bh (b = base and h = height)

Trapezoid Area = ½ h (b1 + b2)

Rhombus Area = ½d1d2 (d = diagonal)

You can justify the area formula for parallelograms as follows:

hThe area of a

parallelogram is the area of a rectangle with the same base

and height.

Area of Parallelogram = bh

Ex 3: Find the area of parallelogram ABCD

A

B C

D

E

F12

16

9

12

Method 1Use AB as the base and

BE as the height.

2144

)9(16

unitsA

A

bhA

Ex 3: Find the area of parallelogram ABCD

A

B C

D

E

F12

16

9

12

Method 2Use AD as the base

and CF as the height.

2144

)12(12

unitsA

A

bhA

You get the same answer.

Ex 4: Find the area of trapezoid WXYZ.

X(1, 1) W(8, 1)

Z(5, 5)Y(2, 5)

2

21

20

)40(2

1

)10)(4(2

1

)73)(4(2

1

)(2

1

unitsA

A

A

A

bbhA

Count the blocks for height, base 1, and base 2.

Ex 5:The area of a trapezoid is 135 cm2, height is 9, and one bases is 11. Find the other base.

xcm

x

x

x

x

bbhA

19

9171

999270

)11)(9(270

)11)(9(2

1135

)(2

121

Ex 6: Find the area of the rhombus.

9

912 12

2

21

216

)432(2

1

)24)(18(2

12

1

unitsA

A

A

ddA

Ex 7: The area of a rhombus is 40 in2 and one of the diagonals is 8 in. Find

the other diagonal.

2

2

2

21

10

440

)8(2

140

2

1

d

d

d

ddA

Ex 8: Find the area if the radius .38

192

)364(

)38( 2

2

A

A

A

rA

Leave your answer in terms of pi unless stated otherwise.

38

Circle Area = 2r