1. Review Slides for Final on May 30th
This slide show is designed to help you prepare for your final on May 30th.
Topics covered are area, volume and surface area of complex shapes. Angles, right, obtuse and acute will also be covered.

2. Area
You will need to be able to find the area of a triangle, square, rectangle, and trapezoid. In addition you will need to be able to look at a complex shape and use your knowledge of simple shapes to find the area, surface area and volume of the complex shapes.

3. Area
When working with area we must remember that we are referring to the inside of a shape or figure. This is different than perimeter that looks at the distance around the outside of a shape or figure.
The area of the rectangle is
9 x 4 or 36 units squared,
because there are 36 1 X 1
smaller squares inside. The formula is L X W
The perimeter would be =
26units. Notice it is not squared. This
would be like building a fence around the
rectangle. The formula is L + W + L + W
9 units
4 units

4. Area
Math contains many patterns and relationships. This slide addresses the relationship between rectangles and triangles.
How many triangles are inside of the rectangle?
Knowing that a triangle is ½ of a rectangle or square we can deduce that the formula for area of a triangle is L X W . Once again we are talking about square area. 2

5. Surface area
When we represent 3 dimensional shapes and objects on paper we have to let our eyes imagine in 3 dimensions. For this slide looking at a 3 dimensional figure may help you see what the figure is conveying. Pick up a shoe box. How many flat surfaces can you identify?

6. Surface area Continued
To find the surface area you need to identify all six sides. The front side is equal to the back and the side to the opposing side. Finally the top and bottom should have equal dimensions. To find the surface area simply find the area of each side and then add them together.

7. Surface Area
There are two squares on the front and back 3 X 3 = 9, now multiply it by 2 = 18 units squared There are four 8 X 3 rectangles which are the two sides and top and bottom. 8 X3 = 24 units squared. Multiply 24 X 4 and you have 96 units units squared. Now add 96 to 18 for a total surface area of 114 units squared.
8 units
9 units
3 units
3 units

8. Practice Find the area 8 inches squared 5 inches squared

9. Find the Surface area
11 inches
6 inches
6inches

10. Find the Volume
11 inches
11 inches
6 inches
6 inches
6 inches
6inches

11. More Complex Shapes
Knowing how to find the area and volume of simple shapes can help us break down more complex shapes. For example a trapezoid.
We can see that we have two triangles and a rectangle.

12. More Complex Shapes
There are different ways to approach solving this problem. One would be to find the area of the rectangle and the two triangles and add them. If the triangles have equal bases you could combine the triangle into a square.

13. Practice
Find the area of the figure. Assume the triangles on either side have equal bases.
9 inches
6inches
20 inches

14. Angles There are three types of angles that you need to know.
Right angles are angles with a 90 degree angle.
Obtuse angles are angles that are greater than 90 degrees.
Acute angles are angles that are less than 90 degrees.