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 Trianglesh b
Area of rectangle = bh
Area of parallelogram = bh
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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
A = 11(16)
Substitute 11 for b and 16 for h.
A = 176 mm2
Simplify.
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
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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
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6. 10.1 Area of Parallelograms and Triangles
Area ∆ = ½ bh h b b1
Area trap. = ½(b1 + b2)h h b2
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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.
A = 40.3 in2
Simplify.
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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.
Multiply both sides by
6x = b
b = 6x cm
Sym. Prop. of =
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9. 10.1 Area of Parallelograms and Triangles
Area = ½d1d2
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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.
282 + y2 = 352
212 + x2 = 292
x2 = 400
y2 = 441
x = 20
y = 21
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.
Area of kite
A = 1008 in2
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11. Objectives 10.2 Area of Circle
Develop and apply the formulas for the area and circumference of a circle.
10-2

12. 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. Area of Circle
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14. 10.2 Area of Circle Find the area of K in terms of . A = r2
Area of a circle.
Divide the diameter by 2 to find the radius, 3.
A = (3)2
A = 9 in2
Simplify.
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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.
A = r2
Area of a circle
25x2 = r2
Substitute 25x2 for A.
25x2 = r2
Divide both sides by .
5x = r
Take the square root of both sides.
Step 2 Use the value of r to find the circumference.
C = 2r
C = 2(5x)
Substitute 5x for r.
C = 10x ft
Simplify.
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16. 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
≈ cm2
≈ cm2
≈ cm2
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17. HOMEWORK:
10.1(682):11-17,23-25,30-33
10.2(691):10-13,34-37