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.