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

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Presentation on theme: "Area and Perimeter 1.6 What does the area of a figure measure?"— Presentation transcript:

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

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

3 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.)

4 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

5

6 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.

7 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

8 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

9 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).

10 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 or about 25 units.

11 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 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

12 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.

13 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


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