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10.1 Area of Parallelograms and

Triangles

Objective

Develop and apply the formulas for the areas of

triangles and special quadrilaterals. Solve

problems involving perimeters and areas of

triangles and special quadrilaterals.

10-1

10.1 Area of Parallelograms and

Triangles

h

b

Area of rectangle bh

Area of parallelogram bh

10-1

10.1 Area of Parallelograms and

Triangles

Find the area of the parallelogram.

Step 1 Use the Pythagorean Theorem to find the

height h.

302 h2 342

h 16

Step 2 Use h to find the area of the

parallelogram.

Area of a parallelogram

A bh

Substitute 11 for b and 16 for h.

A 11(16)

Simplify.

A 176 mm2

10-1

10.1 Area of Parallelograms and

Triangles

Find the height of a rectangle in which b 3 in.

and A (6x² 24x 6) in2.

A bh

Area of a rectangle

Substitute 6x2 24x 6 for A and 3 for b.

6x2 24x 6 3h

10-1

10.1 Area of Parallelograms and

Triangles

Find the base of the parallelogram in which h

56 yd and A 28 yd2.

A bh

Area of a parallelogram

28 b(56)

Substitute.

Simplify.

b 0.5 yd

10-1

10.1 Area of Parallelograms and

Triangles

Area ? ½ bh

h

b

b1

Area trap. ½(b1 b2)h

h

b2

10-1

10.1 Area of Parallelograms and

Triangles

Find the area of a trapezoid in which b1 8 in.,

b2 5 in., and h 6.2 in.

Area of a trapezoid

Substitute 8 for b1, 5 for b2, and 6.2 for h.

Simplify.

A 40.3 in2

10-1

10.1 Area of Parallelograms and

Triangles

Find the base of the triangle, in which A

(15x2) cm2.

Area of a triangle

Substitute 15x2 for A and 5x for h.

Divide both sides by x.

6x b

Sym. Prop. of

b 6x cm

10-1

10.1 Area of Parallelograms and

Triangles

Area ½d1d2

10-1

10.1 Area of Parallelograms and

Triangles

Find the area of the kite

Step 1 The diagonals d1 and d2 form four right

triangles. Use the Pythagorean Theorem to find x

and y.

212 x2 292

282 y2 352

x2 400

y2 441

x 20

y 21

Area of kite

Step 2 Use d1 and d2 to find the area. d1 is

equal to x 28, which is 48. Half of d2 is equal

to 21, so d2 is equal to 42.

A 1008 in2

10-1

10.2 Area of Circle

Objectives

Develop and apply the formulas for the area and

circumference of a circle.

10-2

10.2 Area of Circle

You can use the circumference of a circle to find

its area. Divide the circle and rearrange the

pieces to make a shape that resembles a

parallelogram.

The base of the parallelogram is about half the

circumference, or ?r, and the height is close to

the radius r. So A ? ? r r ? r2.

The more pieces you divide the circle into, the

more accurate the estimate will be.

10-2

10.2 Area of Circle

10-2

10.2 Area of Circle

Find the area of ?K in terms of ?.

Area of a circle.

A ?r2

Divide the diameter by 2 to find the radius, 3.

A ?(3)2

Simplify.

A 9? in2

10-2

10.2 Area of Circle

Find the circumference of ?M if the area is 25

x2? ft2

Step 1 Use the given area to solve for r.

Area of a circle

A ?r2

Substitute 25x2? for A.

25x2? ?r2

Divide both sides by ?.

25x2 r2

5x r

Take the square root of both sides.

Step 2 Use the value of r to find the

circumference.

C 2?r

Substitute 5x for r.

C 2?(5x)

Simplify.

C 10x? ft

10-2

10.2 Area of Circle

A pizza-making kit contains three circular baking

stones with diameters 24 cm, 36 cm, and 48 cm.

Find the area of each stone. Round to the nearest

tenth.

24 cm diameter

36 cm diameter

48 cm diameter

A ?(12)2

A ?(18)2

A ?(24)2

452.4 cm2

1017.9 cm2

1809.6 cm2

10-2

HOMEWORK 10.1(682)11-17,23-25,30-33 10.2(691)10

-13,34-37