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Developing Formulas for Triangles and QuadrilateralsGeometry H2 (Holt 10-1) K. Santos
Area of a ParallelogramArea = product of its base and height A= bh Base must be perpendicular to the height b h 5cm 3cm 9cm
Example Find the perimeter of a parallelogram, in which the base is 4ft and the area is 12 𝑓𝑡 2 .
Area of a Triangle Area = one half of the product of its base and height A= 1 2 bh or A = 𝑏ℎ 2 Base perpendicular to height h h h b b b If b = 4” and h = 6”
Example—finding a sideThe area of a triangle is 24 𝑐𝑚 2 and its height is 3 cm. Find the length of its corresponding base.
Area of a Trapezoid Area = (average of the bases)(height) A = 𝑏 1 + 𝑏 2 2 h 𝑏 1 h 𝑏 2 Remember: height is perpendicular to both bases
Example 1--Trapezoid Find the area of the trapezoid. 20 in 25 in 18 in 36 in
Example 2--Trapezoid Find the area of the trapezoid. 11 ft 13 ft 16 ft
Area of a Rhombus The area of a rhombus is half the product of the lengths of its diagonals. A = 𝑑 1 𝑑 2 2 𝑑 2 𝑑 1 Example: Find the area if the diagonals are: 6 in and 8 in
Area of a Kite The area of a kite is half the product of the lengths of its diagonals. 𝑑 1 A = 𝑑 1 𝑑 2 2 𝑑 2 Example 1: Kite with diagonals 9 cm & 8 cm
Example 2--Kite Find the area of the kite. 5” 4” A = 𝑑 1 𝑑 2 2 6”
Formulas Square: A = bh Rectangle: A = bh Parallelogram: A = bh Trapezoid: A = 𝑏 1 + 𝑏 2 2 h Triangle: A = ½ bh Rhombus: A = 𝑑 1 𝑑 2 2 Kite: A = 𝑑 1 𝑑 2 2
Area Addition PostulateThe area of a region is equal to the sum of the areas of its nonoverlapping parts. Best way to find this area is to find the area of rectangle + area of triangle
Example—Partitioning ShapesFind the area of the shape below: Find the sum of the areas of the rectangle and the triangle
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