Area and Perimeter Unit Area of 2-D Shapes 2 Squares and Rectangles s s A = s 6 6 A = 6 = 36 sq. units b h A = bh 12 5 A = 12 x 5 = 60 sq. units Example: Area of Rectangle: A = bh Area of Square: A = s 3 Circles and Sectors r 9 cm A = (9) = 81 sq. cm Area of Circle: A = r arc r B C A 120 Example: 9 cm 4 Triangles and Trapezoids h h h b b b1b1 b2b2 h is the distance from a vertex of the triangle perpendicular to the opposite side. h is the distance from b 1 to b 2, perpendicular to each base 5 Example: Triangles and Trapezoids Example: First: Find the height. The height bisects the base. So, b=6. Now we need to find the missing side. IDEAS???? * hint: we are now working with a right triangle. We know 2 of its sides. THATS RIGHT!!! Pythagorean Theorem a+b=c 6+x=10 36+x=100 x=64 x=8 7 Parallelograms & Rhombi Area of Parallelogram: A = bh 6 9 A = 9 x 6 = 54 sq. units 8 10 A = (8)(10) = 40 sq units h b Example: 8 Area of Regions The area of a region is the sum of all of its non-overlapping parts. A=bh A = (8)(10) A= 40 A=bh A = (12)(10) A= 120 A=bh A = (4)(8) A=32 A=bh A = (14)(8) A=112 Area = = 304 sq. units Examples: Cut the shape into several basic shapes. A B C Section A A=bh A=4*5 A=20 cm Section B A=bh A=3*5 A=15 cm Section C A=s A=3 A=9 cm Whole shape= = 44 cm Terms to Know: For any regular polygon : Radius : is a segment joining the center to any vertex Apothem : is a segment joining the center to the midpoint of any side and is also perpendicular to the side. Area of a regular polygon: Remember all angles are congruent and all sides are congruent. Regular pentagon: O is the center OA the radius OM is an apothem N T A O M E P Apothems Facts : 1.All apothems of a regular polygon are congruent. 2.Only regular polygons have apothems. 3.An apothem is the perpendicular bisector of a side. 13 Areas of Regular Polygons Perimeter = (6)(8) = 48 apothem = Area = (48)( ) = sq. units 8 A reg. poly = a p Area of a regular polygon equals one-half the product of the apothem and the perimeter. Where : a = apothem p = perimeter