how much paint do we need to paint all the rooms in our house? bedroom kitchen tv room
TRANSCRIPT
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