Post on 04-Jan-2016
description
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