1. Today we will derive and use the formula for the area of a triangle by comparing it with the formula for the area of a rectangle. derive = obtain or receive

2. This is a right triangle. A triangle is a polygon with three sides and three angles. What happens when you invert the triangle? What happens if you put them together? What shape does it make? It forms a rectangle. Rectangles are shapes that have four sides – two pairs of sides with equal lengths.. Rectangle!

3. What happens if we create a triangle from this rectangle? And we cut out the sides of the triangle out? And we put them on the triangle that is left. What conclusion can we draw?

4. Let us try this! 1.Cut outside of the black lines. 2.After cutting outside the black lines, place them inside the new triangle. 3.What conclusions can you draw from doing this exercise?

5. Formula A formula is a math rule used to solve specific problems.

6. Formula for deriving the area of a triangle. One half the base time the height. Let’s see what that looks like! Formula for deriving the area of a rectangle. The base time the height. Let’s see what that looks like 12 inches 6 inches =36 12 inches 6 inches =72

7. What is the area of this rectangle? 7 units 10 units Area of a rectangle is Length x the Width 10 units x 7 units = 70 units squared

8. What is the area of this triangle? 7 units 10 units Area of a triangle is ½ Length x the Width 10 units x 7 units = 35 units squared

9. Let’s look at some more triangles 10 inches 11 inches Area = ½ base times the height =55

10. Why else is it important to use the distributive property in equations and expressions with variables It is important to derive and use the formula to figure out the area of a triangle because it will help you on your test. It will also prepare you for junior and high school.

11. We are going to use the formula for finding the area of triangles. 1.Look at the base of the triangle 2.Look at the height of the triangle 3.Remember the formula for finding the area of triangles ½ B x H 4.Put in the numbers in the formula 5.½ (5 x 14)=35 14 ft 5 ft

12. We are going to use the formula for finding the area of triangles. 1.Look at the base of the triangle 2.Look at the height of the triangle 3.Remember the formula for finding the area of triangles ½ B x H 4.Put in the numbers in the formula 5.½ (8 ft x 4ft)=12 ft ² 4 ft 8 ft

13. We are going to use the formula for finding the area of triangles. 1.Look at the base of the triangle 2.Look at the height of the triangle 3.Remember the formula for finding the area of triangles ½ B x H 4.Put in the numbers in the formula 5.½ (4 ydsx 12 yds)=24 yds ² 12 yds 4 yds

14. We are going to use the formula for finding the area of triangles. 1.Look at the base of the triangle 2.Look at the height of the triangle 3.Remember the formula for finding the area of triangles ½ B x H 4.Put in the numbers in the formula 5.½ (1cm x 18cm)=9cm ² 18 cm 1 cm

15. Let’s review what we learned: What is the formula for the area of a rectangle? Why is the formula for the area of a triangle? What do you think is the most important reason to know how use the formula for solving the area of a triangle?