geometry 11.1 big idea: compute areas of triangles and parallelograms
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Geometry 11.1 Big Idea: Compute Areas of Triangles and Parallelograms. Postulate 24: Area of a Square. Postulate 25: Area Congruence If 2 polygons are congruent, then they have the same area. Area ABCD = Area PQRS. Postulate 26: Area Addition - PowerPoint PPT PresentationTRANSCRIPT
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?