Chapter 7 Chapter 7 Lesson 1Lesson 1

Objective:Objective: To find the To find the area of a parallelogram area of a parallelogram

and a triangle.and a triangle.

Theorem 7-1Theorem 7-1Area of a RectangleArea of a Rectangle

The area of a rectangle is the The area of a rectangle is the product of its base and height. product of its base and height.

AA = = bhbh

hh

bb

Theorem 7-2Theorem 7-2Area of a ParallelogramArea of a Parallelogram

The area of a parallelogram The area of a parallelogram is the product of a base and is the product of a base and the corresponding height. the corresponding height.

AA = = bhbh

A base of a parallelogram is any of its sides. The corresponding altitude is a segment perpendicular to the line containing that base drawn from the side opposite the base. The height is the length of an altitude.

Example 1: Example 1: Finding the Area of a Finding the Area of a ParallelogramParallelogram

Find the area of each parallelogram.  

Example 2: Example 2: Finding the Area of a Finding the Area of a ParallelogramParallelogram

Find the area of a parallelogram with base 12 m and height 9 m.

A=bhA=bh

A=(12)(9)A=(12)(9)

A=108mA=108m22

Example 3: Example 3: Finding Area in the Coordinate PlaneFinding Area in the Coordinate Plane

Finding Area in the Coordinate PlaneFind the area of parallelogram PQRS with vertices P(1, 2), Q(6, 2), R(8, 5), and S(3, 5). Graph parallelogram PQRS. If you choose      as the base, then the height is 3.

Example 4: Example 4: Finding Area in the Coordinate Finding Area in the Coordinate PlanePlane

Find the area of parallelogram EFGH with vertices E(–4,

3), F(0, 3), G(1, –2), and H(–3, –2).

22 44-2-2-4-4

22

44

-2-2

-4-4

44

55A=bhA=bh

A=(4)(5)A=(4)(5)

A=20 unitsA=20 units22

Example 5: Example 5: Finding a Missing Finding a Missing DimensionDimension

For parallelogram ABCD, find CF to the nearest tenth.First, find the area of parallelogram ABCD.

Then use the area formula a second time to find CF.

AssignmentAssignment•Page 351-353•#1-10; 36; 37;

42; 43

A diagonal divides any A diagonal divides any parallelogram into two congruent parallelogram into two congruent

triangles. triangles.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                   

Therefore, the area of each Therefore, the area of each triangle is half the area of the triangle is half the area of the

parallelogram.parallelogram.

Theorem 7-3  Area of a Triangle

The area of a triangle is half the product of a base and the

corresponding height. A = ½bh

A A base of a trianglebase of a triangle is any of its sides. The is any of its sides. The corresponding height is the length of the altitude corresponding height is the length of the altitude

to the line containing that base. to the line containing that base.

Example 6: Example 6: Finding the Area of a TriangleFinding the Area of a Triangle

Find the area of the shaded triangle. Find the area of the shaded triangle.

The area of the shaded triangle is 32 ftThe area of the shaded triangle is 32 ft22

Example 7: Example 7: Finding the Area of a TriangleFinding the Area of a Triangle

Find the area of the triangle.Find the area of the triangle.

                           

A= ½ bhA= ½ bh

A= ½ (12)(5)A= ½ (12)(5)

A= 30cmA= 30cm22

Example 8: Example 8: Real World ConnectionReal World Connection

Find the area of the figure.

triangle area = ½bh =½(20)6 = 60 ft2 rectangle area = bh = 20(12) = 240 ft2 area of the side = 60 + 240 = 300 ft2

AssignmenAssignmentt

Pg.352-353 #11-23; 38-

41; 44-46