Area and Perimeter 1.6 What does the area of a figure measure? What does the perimeter of a figure measure?

Identify and name polygons. Find perimeter, circumference, and area of two-dimensional figures.

Definition He put a fence on the perimeter of the property. Perimeter of a polygon—the sum of the lengths of the sides of the polygon (add the length of the sides). Circumference of a circle is the distance around the circle. Perimeter and circumference are the distance around the figure. It is measured in linear units (like inches or centimeters.)

Definition He measured the room and then figured the area of the floor for the new carpet. Area: the number of square units needed to cover the surface (in a plane region). 1 2 3 4 5 6 7 8

Area Postulates For every polygonal region, there is a unique positive number called the area of the region. If two polygonal regions are congruent, then they have equal areas.

Theorems The circumference of a circle is the product of π and its diameter d. C = πd The circumference of a circle is twice the product of π and its radius r C = 2πr The area of a circle is the product of π and the square of its radius r. A = π·r2

Find the Perimeter and Area C ≈ 18.85 A ≈ 28.3 20 21 56 P = 80 A = 400 6.2 cm P = 154 A = 1176 C ≈ 18.85 A ≈ 28.3

Perimeter and Area on the Coordinate Plane Find the perimeter and area of a pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1).

Step 1 By counting squares on the grid, we find that CD = 6 units and DE = 5 units. Use the Distance Formula, to find AB, BC, and EA. The perimeter of pentagon ABCDE is 5.7 + 4.1 + 6 + 5 + 4.2 or about 25 units.

Step 2 Divide the pentagon into two triangles and a rectangle. Find the area of the triangles. Area of Triangle 1 Area of a triangle Area of Triangle 2 Substitute. Substitute. Simplify. Simplify. Find the area of the rectangle. The area of pentagon ABCDE is 9 + 2.5 + 30 or 41.5 square units. Answer: The perimeter is about 25 units and the area is 41.5 sq. units. Area of a rectangle Substitute. Simplify. Example 4 Example 4

What does the area of a figure measure? The number of square units contained in a plane region. What does the perimeter of a figure measure? The distance around the figure.

Assignment 1-6 day 2 p. 62, 17-22, 34-39 You must show your equation with the numbers in it to get along with the answer to get credit for the problem. Example: P = 2(3.2) + 2(2.1) = 10.6 A = (3.2)(2.1) = 6.72 NO WORK NO CREDIT