# Area - mrsmeluskey

```How much paint do we need to paint all
the rooms in our house?
kitchen
bedroom
TV
room
Square Area = s2 (s = side length)
Rectangle Area = lw (l = length and w =
width)
Triangle Area = &frac12;bh (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 = &frac12;bh
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 cm
8 cm
A = s2
A = 82
A = 64 cm2
b. A rectangle whose length is 5 m and
width is 11 m.
5m
11 m
11 m
5m
A = lw
A = (5)(11)
A = 55 m2
c. A triangle whose side lengths are 3 in, 4
in, and 5 in.
5 in
4 in
3 in
A = &frac12; (4)(3)
A = &frac12; (12)
A = 6 in2
Ex 2: Find the indicated side length.
a. A square with area 256 in2.
16 in
16 in
16 in
16 in
A = s2
256 = s2
16 = s
b. A rectangle with area 345 ft and length
15 ft.
15 ft
23 ft
23 ft
15 ft
A = lw
345 = 15w
23 ft = w
c. A triangle with area 12 mm and a base
length of 6 mm.
4 mm
6 mm
A = &frac12; bh
12 = &frac12; (6)h
12 = 3h
4 mm = h
Parallelogram Area = bh (b = base and h =
height)
Trapezoid Area = &frac12; h (b1 + b2)
Rhombus Area = &frac12;d1d2 (d = diagonal)
You can justify the area formula for
parallelograms as follows:
h
The 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
B
C
A  bh
9
16
E
12
A  16(9)
A  144units
2
A
12
D
Method 1
Use AB as the base and
BE as the height.
F
Ex 3: Find the area of parallelogram ABCD
C
B
A  bh
9
16
E
12
A  12(12)
A  144units
2
A
12
D
F
Method 2
You get the same
Use AD as the base and
CF as the height.
Ex 4: Find the area of trapezoid WXYZ.
1
A  h(b1  b2 )
2
1
Y(2, 5) Z(5, 5)
A  ( 4)(3  7)
2
1
A  ( 4)(10)
2
1
A  ( 40)
X(1, 1)
W(8, 1)
2
A  20units2
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.
1
A  h(b1  b2 )
2
1
135  (9)(11 x )
2
270  (9)(11 x )
270  99  9 x
171 9 x
19cm  x
Ex 6: Find the area of the rhombus.
9
12
9
12
1
A  d1d 2
2
1
A  (18)(24)
2
1
A  (432)
2
2
A  216units
Ex 7: The area of a rhombus is 40 in2
and one of the diagonals is 8 in. Find
the other diagonal.
1
A  d1 d 2
2
1
40  (8) d 2
2
40  4d 2
10  d 2
Circle Area =
r
2
Ex 8: Find the area if the radius 8 3 .
A  r
8 3
2
A   (8 3 )
A   (64  3)
A  192
2