07.04 Peaks of Patagonia

Areas

In numbers 1 - 8, you are looking for the shaded area, which is gray or tan. The area that you will be subtracting is the light purple area. You will need to calculate the shaded areas and answer in numeric form, not using the symbol for pi

7.04

1) The area of a square + 1/2 the area of a circle

+ = Square Area = Base x Height Square Area = 6 * 6 = 36 Circle Area = π r 2 (3.14 times radius squared) Since the line dividing the circle into a half circle is 6, the radius is 3.

Circle Area = 3 2 π 9 π = 28.27

Half circle area = ½ (9) π = 14.14

7.04

2. The area of a triangle + 1/2 the area of a circle.

Calculate the area of the triangle in the bottom. Find the area of the semicircle πr 2 and add them together.

7.04

2. The area of a triangle + 1/2 the area of a circle.

4 π2 2 = (3.14) (4) = 12.56

12.56/2

= 6.28

5 4

½ 4 * 5 = 10

7.04

3. Find the area of the square and subtract the area of the circle 5 5 5 = 5 2 - π(2.5) 2

7.04

4. Find the area of the shape

.

2 5 + 5 10 = You will either have to cut the odd shape into rectangles; or find the entire rectangle area, and then subtract the piece cut out of it.

7.04

5. Area of circle - 2 x area of triangle with base 16' and height 8'.

16 16 8 X 2 = Find the circle area, then the square area and that 8' measure is from the center out and also the radius of the circle, then subtract the square from the circle area.

7.04

6. Area of rectangle (10x20) - area of circle with radius of 5.

10 20 10

π5

2 = Find the area of the rectangle (length x width) then subtract the area of the circle. Note: you have to use the radius, and the diameter is given.

7.04

7. 3/4 area of a circle with radius 8‘.

8

π8

2

=

200.96

Find the circle area and either take 75% of it, or 3/4 of it, or subtract 25% or 1/4 of it.

7.04

8. Area of circle with radius 10' - area of circle with radius 4'.

Note the area of the big circle uses a radius of 4+6, so find the area of the big circle and subtract the area of the smaller one whose radius is 4.

9. The probability that a randomly thrown dart will hit the outer green ring of the target from the example in the lesson on Multiple Figures – Shaded Areas.

1 2 2 2 2 Find the area of the dartboard -> radius 9 < Subtract all but the green, -> 9-2 radius <-. The probability would be the area of the green ring, divided by the area of the entire target. 9 2 (9 2 π = all area π - 7 2 π) = area of outer green ring Take that and put it over the entire area.

-> Green ring/entire board = ?% 7.04

7.04

10. Where might you see these shapes in your community  1) 2) 3) 4) 5) 6) 7) 8)