1. CAHSEE PREP.
Week 3
Measurement and Geometry
Valley OFL Prep Sessions

2. Formulas You Must Know:
Perimeter of a Polygon = add up the sides
Circumference of a Circle = πd where
d = diameter
Area of a parallelogram = bh where
b = base and h = height
Area of a triangle = ½ bh where

3. Formulas You Must Know:
Volume of a rectangular solid = lwh where
l = length, w = width, and h = height
Area of a trapezoid = ½ (b1 + b2) h where
(b1 + b2) = sum of the bases
h = height.

4. Area
Carlos needs to tile his kitchen. The dimensions of the kitchen are shown. What is the area of the kitchen in square feet?
10 ft
6.4 ft
h = 6 ft

5. All measurements in Feet
Area 90
Amy is creating a flower bed. She wants to plant flowers around the perimeter of both figures. What will be the total length of her flower bed?
What is the area of the shaded region?
What is the area of the unshaded region? 13 13 30 5 12
All measurements in Feet

6. Circles What is the perimeter of the circle?
What is the area of the circle?
10 feet

7. What is the area of the shaded region?
Jason and Paul are running a race. If Paul runs around the inside circle twice and Jason runs around the outside circle once, who has run the farthest?
What is the area of the shaded region?
5 feet
10 feet

8. Trapezoid Find the area of the figure. 10 feet 20 feet
Height is 5 feet.

9. Surface Area = area of the surface of a figure.
1.5 feet
4 feet
Find the surface area of a cylinder. The radius is 1.5 feet and the height is 4 feet. Surface area of a cylinder = 2πr2 + 2πrh.

10. Volume = amount of space inside an object
Find the Volume of the box.
Find the surface area of the box.
3 feet
5 feet
8 feet

11. Practice
In the figure, the radius of the circle is 6 feet. What is the perimeter of the square?
In the above figure, the radius of the circle is 6 feet. What is the area of the shaded region?
It costs $2.25 per square foot for carpeting. How much will it cost to carpet the shaded region?

12. You should memorize these facts and know how to use the conversions!
Converting Units
Metric:
Kilo means 1000 so 1 kg = 1000 grams
Centi means 1/100th, so 100 cm = 1 m
Milli means 1/1000th, 1000 mm = 1 m
Standard system:
1 foot = 12 inches
1 yard = 3 feet
1 mile = 5280 feet
1 cup = 8 ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 pound = 16 ounces
1 ton = 2000 pound
You should memorize these facts and know how to use the conversions!

13. Practice
A bottle of water is 32 ounces. How many cups of water does it hold?
Jason buys 300 liters of juice. How many 500 mL bottles can he fill with juice?

14. Pythagorean Theorem If a = 3 and b = 4, what is the value of c?
If a triangle has a hypotenuse with a length of 8 feet and one leg has a length of 4 feet, how long is the remaining leg? a b c
a2 + b2 = c2

15. Similar Figures:
The two triangles are similar. What is the value of x?
10 in.
8 in
5 in x

16. Similar Figures:
The two triangles are similar. Find the values of x and y.
10 in.
8 in
5 in x
6 in. y