10.1 Area of Parallelograms and Triangles - PowerPoint PPT Presentation

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10.1 Area of Parallelograms and Triangles

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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. – PowerPoint PPT presentation

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Title: 10.1 Area of Parallelograms and Triangles


1
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
2
10.1 Area of Parallelograms and
Triangles
h
b
Area of rectangle bh
Area of parallelogram bh
10-1
3
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
4
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
5
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
6
10.1 Area of Parallelograms and
Triangles
Area ? ½ bh
h
b
b1
Area trap. ½(b1 b2)h
h
b2
10-1
7
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
8
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
9
10.1 Area of Parallelograms and
Triangles
Area ½d1d2
10-1
10
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
11
10.2 Area of Circle
Objectives
Develop and apply the formulas for the area and
circumference of a circle.
10-2
12
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
13
10.2 Area of Circle
10-2
14
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
15
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
16
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
17
HOMEWORK 10.1(682)11-17,23-25,30-33 10.2(691)10
-13,34-37
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