G1.4.1: Solve problems involving area and perimeter of quadrilaterals.

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Presentation transcript:

G1.4.1: Solve problems involving area and perimeter of quadrilaterals. 5.1: Perimeter and Area Expectation: G1.4.1: Solve problems involving area and perimeter of quadrilaterals. 4/24/2017 5.1: Perimeter and Area

ABCD is a parallelogram whose diagonals intersect at E ABCD is a parallelogram whose diagonals intersect at E. If AE = 2x + 1, CE = 4x – 11 and BD = 18, what is the value of AC? 6 9 13 18 26 4/24/2017 5.1: Perimeter and Area

Perimeter Defn: The perimeter of a closed figure is the distance around the figure. 4/24/2017 5.1: Perimeter and Area

Area Defn: The area of a closed figure is the number of non-overlapping squares of a given size that will exactly cover the interior of the figure. 4/24/2017 5.1: Perimeter and Area

Area = 21 unit squares so we say the area is 21 square units. 4/24/2017 5.1: Perimeter and Area

Sum of Areas Postulate If a figure is composed of nonoverlapping regions A and B, then the area of the figure is the sum of the areas of regions A and B. 4/24/2017 5.1: Perimeter and Area

A1 = 25 sq units A2 = 35 sq units Total Area = 25 + 35 = 60 sq units Sum of Areas Postulate A1 = 25 sq units A2 = 35 sq units Total Area = 25 + 35 = 60 sq units 4/24/2017 5.1: Perimeter and Area

Perimeter of a Rectangle Formula If a rectangle has perimeter P units, a base of b units and height of h units, then P = 2b + 2h. The more common formula is: P = 2l + 2w 4/24/2017 5.1: Perimeter and Area

Area of a Rectangle Postulate If a rectangle has area of A square units, base of b units and height of h units, then A = bh (or A = lw). 4/24/2017 5.1: Perimeter and Area

Estimating the area of irregular figures We will call a unit square entirely inside the figure an interior square and any unit square which contains a part of the figures’ boundary a boundary square. 4/24/2017 5.1: Perimeter and Area

Estimating the area of irregular figures 1. Count the total number of interior squares (i). 2. Count the total number of boundary squares (b). 3. Estimate = i + .5b 4/24/2017 5.1: Perimeter and Area

Estimate the area of the figure below. 4/24/2017 5.1: Perimeter and Area

A farmer has 100 feet to fence in a pen for baby animals A farmer has 100 feet to fence in a pen for baby animals. What are the dimensions of the rectangle that will give her the maximum area? 4/24/2017 5.1: Perimeter and Area

A gardener wants to make a rectangular garden that has an area of 150 square feet, but he wants to minimize the amount of fencing required to enclose the garden. What should the dimensions of the garden be? 4/24/2017 5.1: Perimeter and Area

A rectangular lot that measures 125 feet by 185 feet is completely fenced. What is the length, in feet, of the fence? 310 435 620 740 1,240 4/24/2017 5.1: Perimeter and Area

The length of a side of a square is represented by (3x-2) inches The length of a side of a square is represented by (3x-2) inches. Which of the following general expressions represents the area of the square, in square inches? 12x – 8 9x2 – 4 9x2 – 6x + 4 9xx – 12x – 4 9x2 – 12x + 4 4/24/2017 5.1: Perimeter and Area

Assignment pages 299 – 302, #9-14, 20-28 (evens), 32-36 (all) and 39. 4/24/2017 5.1: Perimeter and Area