Transcript 5-2A Assumptions About Area

11-1 Area of Parallelograms and
Triangles
You found areas of rectangles and squares.
• Find perimeters and areas of parallelograms.
• Find perimeters and areas of triangles.
Definitions
A quadrilateral is a polygon with four sides.
A parallelogram is a
quadrilateral with two
pairs of parallel sides.
A rectangle is a
quadrilateral with
four right angles.
A square is a
quadrilateral with
four right angles
and four congruent
sides.
What is the formula for the area of
a rectangle?

A=l×w
w
l
In the Area…
Use the paper parallelogram, and label a
base and height as shown. By cutting and
rearranging pieces, use the area formula
for a rectangle to help find the area
formula for a parallelogram in terms of the
length of the base and the height.
h
b

The area of a rectangle is the product of
its length (l) and width (w).
A = lw
w
l

The are of a square is the square of its
side length (s).
2
A=s
s
p. 779

The area of a parallelogram is the product
of its base length (b) and height (h).
A = bh
h
b
p. 779
Find the perimeter and area of
Perimeter
Since opposite sides of a parallelogram
are congruent, RS UT and RU ST.
So UT = 32 in. and ST = 20 in.
Perimeter = RS + ST + UT + RU
Area
= 32 + 20 + 32 + 20 = 104 in.
Find the height of the parallelogram. The height
forms a right triangle with points
S and T with base 12 in. and hypotenuse 20 in.
c2
= a2 + b2
Pythagorean Theorem
202 = 122 + b2
c = 20 and a = 12
400 = 144 + b2
Simplify.
256 = b2
Subtract 144 from each side.
16 = b
Take the positive square
root of each side.
The height is 16 in. UT is the base, which measures
32 in.
A = bh
= (32)(16) or 512 in2
Area of parallelogram
b = 32 and h = 16
Answer: The perimeter is 104 in. and the area is
512 in2.
A. Find the perimeter and area of
A. 88 m; 255 m2
B. 88 m; 405 m2
C. 88 m; 459 m2
D. 96 m; 459 m2
p. 781

The area of a triangle is half the product
of its base length (b) and corresponding
height (h).
A = ½bh
h
b
p. 781
SANDBOX You need to buy
enough boards to make the
frame of the triangular sandbox
shown and enough sand to fill it.
If one board is 3 feet long and
one bag of sand fills 9 square
feet of the sandbox, how many
boards and bags do you need to
buy?
Step 1 Find the perimeter of the sandbox.
Perimeter = 16 + 12 + 7.5 or 35.5 ft
Step 2
Find the area of the sandbox.
Area of a triangle
b = 12 and h = 9
Step 3
Use unit analysis to determine how many of
each item are needed.
Boards
boards
Bags of Sand
Round the number of boards up so there is enough
wood.
Answer:
You will need 12 boards and 6 bags of sand.
Find the area of the figure.
7
4
49
24.6
12.3
7
35.26 4.3
8.2
What is a…
quadrilateral?
A quadrilateral is a polygon with four sides.
 parallelogram?
A parallelogram is a quadrilateral with two pairs
of parallel sides.
 rectangle?
A rectangle is a quadrilateral with four right
angles.
 square?

A square is a quadrilateral with four right angles
and four congruent sides.
Area Formulas
 Rectangle
A = lw

Square
A = s2

Triangle
A = ½bh

Parallelogram
A = bh
11-1 Assignment
Page 10-15
No formulas with numbers,
no credit for the problem.