1. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Expectations:
G1.2.2: Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles.
G2.1.1: Know and demonstrate the relationships between the area formula of a triangle, the area formula of a parallelogram, and the area formula of a trapezoid.
G2.1.2: Know and demonstrate the relationships between the area formulas of various quadrilaterals (e.g., explain how to find the area of a trapezoid based on the areas of parallelograms and triangles).
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

2. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Anatomy of a Triangle
Any side of a triangle can be the base of the triangle. An altitude of the triangle is a segment that is perpendicular to the line containing the base. There are 3 pairs of corresponding bases and altitudes for any triangle. The height of a triangle is the length of a particular altitude (relative to the length of a base).
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

3. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Anatomy of a Triangle
altitude
base
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

4. 5.2: Areas of Triangles, Parallelograms and Trapezoids
altitude
base
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

5. 5.2: Areas of Triangles, Parallelograms and Trapezoids
altitude
base
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

6. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Bases and Altitudes
The base must be a side of the triangle, but the altitude does not have to be. In fact, the only triangles that have altitudes that are actual sides of the triangle are right triangles.
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

7. Area of a Right Triangle
Use the area of a rectangle formula to justify the area of a right triangle formula.
A = .5bh = .5ab
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

8. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Area of Any Triangle
If a triangle has a base of length b units and a height of h units, then the area of the triangle, A, is given by the formula:
A = .5bh
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

9. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Use either the area of a rectangle formula or the area formula for a right triangle to justify the area of a triangle formula.
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

10. Anatomy of a Parallelogram
Any side of a parallelogram can be the base. The altitude of a parallelogram is a segment with its endpoints on the lines containing the bases, perpendicular to the bases. The height of the parallelogram is the length of the altitude.
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

11. 5.2: Areas of Triangles, Parallelograms and Trapezoids
base 2
altitude
base 1
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

12. 5.2: Areas of Triangles, Parallelograms and Trapezoids
base 1
base 2
altitude
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

13. Area of a Parallelogram
Using previous formulas, try to figure out the formula for the area of a parallelogram.
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

14. Area of a Parallelogram
If a parallelogram has bases of b units and a height of h units, then its area, A, is given by the formula:
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

15. 5.2: Areas of Triangles, Parallelograms and Trapezoids
The parallel sides of a trapezoid are its bases. The nonparallel sides are the legs. A perpendicular segment from one base to the other is an altitude for the trapezoid. The length of the altitude is the height of the trapezoid
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

16. 5.2: Areas of Triangles, Parallelograms and Trapezoids
base 1
altitude
leg
leg
base 2
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

17. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Using known formulas, try to determine the formula for the area of a trapezoid. Be careful that you do not limit your formula to only isosceles trapezoids.
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

18. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Area of a Trapezoid
If a trapezoid has bases of b1 and b2 units and a height of h units, then the area, A, of the trapezoid is given by the formula:
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

19. Lengths are shown in inches on the drawing of the rectangle below
Lengths are shown in inches on the drawing of the rectangle below. What is the shaded area, in square inches? 18 24 57 78 96 9 2 8 12
4/20/2017
5.1: Perimeter and Area

20. 5.2: Areas of Triangles, Parallelograms and Trapezoids
What is the area of a parallelogram with vertices at (0,0), (2,3), (5,0) and (7,3)? 10 14 15 21 35
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids

21. 5.2: Areas of Triangles, Parallelograms and Trapezoids
Assignment
pages ,
#12, 15, 18, (all), 32, 36, 40, 44, 53
4/20/2017
5.2: Areas of Triangles, Parallelograms and Trapezoids