11-1 Areas of Triangles and Parallelograms Hubarth Geometry.

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Presentation transcript:

11-1 Areas of Triangles and Parallelograms Hubarth Geometry

Postulate Area of a Square Postulate The area of a square is the length of its side squared Area Congruence Postulate If two polygons are congruent, then they have the same area Area Addition Postulate The area of a region is the sum of the area of its nonoverlapping parts. Square all sides are equal and all angles are right angles.

Rectangle opposite sides are equal and all angles are right angles. Theorem Area of a Rectangle The area of a rectangle is the product of its base and height. h b A =bh

Parallelograms opposite side are congruent and opposite angles are congruent. In a parallelogram either pair of sides can be used as the bases of the parallelogram. The height is the perpendicular distance between the bases. h b Theorems Area of a Parallelogram The area of a parallelogram is the product of a base and its corresponding height. A= bh height base

Theorem Area of a Triangle The area of a triangle is one half the product of a base and its corresponding height. height h base b

Method 1 Method 2 Find the area of PQRS. Ex 1 Use a Formula to Find Area

Let h represent the height of the triangle. Then the base is 2h. Ex 2 Solve for the Unknown Measures The base of a triangle is twice its height. The area of the triangle is 36 square inches. Find the base and height h=6 and b=2(6)=12

You can use a right triangle and a rectangle to approximate the area of the side of the barn. 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 3 Solve a Multi-step Problems First, find the base and height of the right triangle. It is an Isosceles triangle so the base and height are the same. We will use the Pythagorean Theorem.

Ex 3 continued Second, find the area of the rectangle portion of the barn. Third, find the area of the entire side of the barn. Lastly, determine how many gallons of paint. So, you will need 2 gallons of paint

Practice 1. Find the perimeter and area of the polygon. a. b. 2. A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base? 3. WHAT IF? In Example 3, suppose there is a 5 foot by 10 foot rectangular window on the side of the barn. What is the approximate area you need to paint? – 50 =587.3 Area of the window = 5(10)=50