geometry 11.1 big idea: compute areas of triangles and parallelograms

Geometry 11.1Geometry 11.1Big Idea: Compute Areas Big Idea: Compute Areas

of Triangles and of Triangles and ParallelogramsParallelograms

Postulate 24: Area of a Square

Postulate 25: Area CongruenceIf 2 polygons are congruent, then they

have the same area.

Area ABCD = Area PQRS

Postulate 26: Area AdditionThe area of a region is the sum of the

areas of its non-overlapping parts.

Area of polygon PQRS=

area of triangle PTS +

area of triangle QUR +

area of PQUT

Theorem 11.1 Area of a RectangleTheorem 11.1 Area of a Rectangle

Area of a rectangle is product of Area of a rectangle is product of base and height (or length and base and height (or length and width).width).

Area = bhArea = bh

Area = lwArea = lw

Vocabulary:Vocabulary:

Bases: Bases: either paireither pair of parallel sides of parallel sides of a parallelogramof a parallelogram

Height: Height: the the perpendicular distanceperpendicular distance between these 2 basesbetween these 2 bases

Theorem 11.2 Area of a Theorem 11.2 Area of a ParallelogramParallelogram

Area of a parallelogram is product of Area of a parallelogram is product of base and its corresponding height.base and its corresponding height.

Area = bhArea = bh

Theorem 11.3 Area of a TriangleTheorem 11.3 Area of a Triangle Area of a triangle is ½ the product of a Area of a triangle is ½ the product of a

base and its corresponding height.base and its corresponding height.

Example: Find the perimeter and area of the polygon.

Example: Find the perimeter and area of the polygon.

Example: Find the perimeter and area of the polygon.

Example: The base of a triangle is twice its height. The area of the triangle is 36 square units. Find the base and the height.

Example: A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base?