Chapter 11.1 Notes: Areas of Triangles and Parallelograms

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Presentation transcript:

Chapter 11.1 Notes: Areas of Triangles and Parallelograms Goal: You will find areas of triangles and parallelograms.

Basic Postulates Postulate 24 Area of a Square Postulate: The area of a square is the square of the length of its side. Postulate 25 Area Congruence Postulate: If two polygons are congruent, then they have the same area. Postulate 26 Area Addition Postulate: The area of a region is the sum of the areas of its nonoverlapping parts.

Rectangles Theorem 11.1 Area of a Rectangle: The area of a rectangle is the product of its base and height. Parallelograms and Triangles In a parallelogram, the parallel sides are called the bases. The height is the perpendicular distance between the bases.

Theorem 11.2 Area of a Parallelogram: The area of a parallelogram is the product of a base and its corresponding height. Theorem 11.3 Area of a Triangle: The area of a triangle is one half the product of a base and its corresponding height.

Ex.1: Find the area of Find the perimeter and area of the polygon. Ex.2: Ex.3:

Ex. 4: Ex. 5: The base of a triangle is twice its height Ex.4: Ex.5: The base of a triangle is twice its height. The area of the triangle is 36 square inches. Find the base and height.

Ex. 6: You need to buy paint so that you can paint the side of a barn Ex.6: You need to buy paint so that you can paint the side of a barn. A gallon of paint covers 350 square feet. How many gallons should you buy? Ex.7: A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base?

Ex.8: Find the area of