11-1 Area of Parallelograms and Triangles You found areas of rectangles and squares. Find perimeters...
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Transcript of 11-1 Area of Parallelograms and Triangles You found areas of rectangles and squares. Find perimeters...
11-1 Area of Parallelograms and 11-1 Area of Parallelograms and TrianglesTriangles
You found areas of rectangles and squares.
• Find perimeters and areas of parallelograms.
• Find perimeters and areas of triangles.
DefinitionsDefinitionsA quadrilateral is a polygon with four sides.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 What is the formula for the area of a rectangle?area of a rectangle?
A = A = l l × × ww
ll
ww
In the Area…In the Area…
Use the paper parallelogram, and label a Use the paper parallelogram, and label a base and height as shown. By cutting base and height as shown. By cutting and rearranging pieces, use the area and rearranging pieces, use the area formula for a rectangle to help find the formula for a rectangle to help find the area formula for a parallelogram in area formula for a parallelogram in terms of the length of the base and the terms of the length of the base and the height.height.
b
h
The area of a rectangle is the product of The area of a rectangle is the product of its length its length (l)(l) and width and width (w).(w).
A = A = lwlw
l
w
The are of a square is the square of The are of a square is the square of its side length its side length (s).(s).
A =A = s s 2 2
s
p. 779
The area of a parallelogram is the The area of a parallelogram is the product of its base length product of its base length (b)(b) and and height height (h).(h).
A = A = bhbh 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.
Area 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.
Perimeter = RS + ST + UT + RU
= 32 + 20 + 32 + 20 = 104 in.
256 = b2 Subtract 144 from each side.
16 = b Take the positive square root of each side.
A = bh Area of parallelogram
= (32)(16) or 512 in2 b = 32 and h = 16
The height is 16 in. UT is the base, which measures 32 in.
Answer: The perimeter is 104 in. and the area is 512 in2.
A. 88 m; 255 m2
B. 88 m; 405 m2
C. 88 m; 459 m2
D. 96 m; 459 m2
A. Find the perimeter and area of
p. 781
p. 781
The area of a triangle is half the The area of a triangle is half the product of its base length product of its base length (b)(b) and and corresponding height corresponding height (h).(h).
A =A = ½½bh bh b
h
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
Bags of Sand
boards
Answer: You will need 12 boards and 6 bags of sand.
Round the number of boards up so there is enough wood.
Find the area of the figure.Find the area of the figure.
7
7 49
8.2
4.335.26
12.3
424.6
What is a…What is a… quadrilateral?quadrilateral?A quadrilateral is a polygon with four A quadrilateral is a polygon with four
sides.sides. parallelogram?parallelogram?A parallelogram is a quadrilateral with two
pairs of parallel sides. rectangle?rectangle?A rectangle is a quadrilateral with four
right angles. square?square?
A square is a quadrilateral with four right angles and four congruent sides.
Area FormulasArea Formulas RectangleRectangle A = A = lwlw
SquareSquare A =A = s s 2 2
TriangleTriangle A =A = ½½bhbh
ParallelogramParallelogram A = A = bhbh
11-1 Assignment11-1 AssignmentPage 10-15Page 10-15
No formulas with numbers, No formulas with numbers, no credit for the problem.no credit for the problem.