Perimeter, Circumference and Area G EOMETRY H ONORS.

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Presentation transcript:

Perimeter, Circumference and Area G EOMETRY H ONORS

polygon – a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints and no two adjacent sides are collinear.

Perimeter of a polygon – sum of the lengths of its sides. Area of a polygon – the number of square units the polygon encloses. Circumference– the perimeter of a circle.

Formulas Perimeter of a square P = 4s Perimeter of a rectangle P = 2b + 2h Circumference of a circle C =  d or C = 2  r

Formulas Area of a square A = s 2 Area of a rectangle A = b  h Area of a circle A =  r 2

Postulates If two figures are congruent, then their areas are equal. The area of a region is the sum of the areas of its nonoverlapping parts.

More Formulas Area of a Triangle A = ½ b  h Perimeter of a Triangle P = a + b + c Area of a parallelogram A = b  h

More Formulas Area of a Trapezoid A = ½ h (b 1 + b 2 )

Example Find the area of this irregular shape. 6 cm 2 cm 24 cm 2 Answer

Y OUR T URN 6 cm 4 cm 2 cm 1 cm 2 cm 20 cm 2 Answer Find the area of this irregular shape.

Y OUR T URN 2 cm 12 cm 8 cm 9 cm 78 cm 2 Answer Find the area of this irregular shape.

Y OUR T URN 12 cm 6 cm 216 cm 2 Answer Find the area of this irregular shape.

PSSA P RACTICE The circumference of a circle equals 31.4 units. What is the circle's diameter? (In this problem, let = 3.14.) A. 15 units B. 10 units C. 5 units D. 2.5 units

PSSA P RACTICE What is the best estimate of the area of the purple figure to the right, in square feet? A.38 square feet B.34 square feet C.26 square feet D.36 square feet

PSSA P RACTICE The perimeter of a rectangle equals 268 units, and its length equals 80 units. What is the width of the rectangle? A. 54 units B. 27 units C. 188 units D. 108 units

PSSA P RACTICE What is the approximate area of the figure to the right? A. 14 B / 2 C. 16 D. 15

PSSA P RACTICE The area of a triangle equals 60.5 square units, and its base equals 11 units. What is the triangle's height? A. 5.5 units B. 33 units C. 11 units D. 22 units

Volume– a measure of space a figure occupies.

More Formulas Volume of a Rectangular Prism V = l  w  h Volume of a Right Cylinder V =  r 2  h Volume of a Right Cone V = 1 / 3  r 2  h

More Formulas Volume of a Sphere Volume of a Rectangular Based Pyramid V = 4 / 3  r 3 V = 1 / 3 l  w  h