Presentation on theme: "Kite Rhombus Trapezoid"— Presentation transcript:
1 Kite Rhombus Trapezoid Section 7-4 Area of Trapezoids, Rhombus, Kites SPI 21B: solve equations to find length, width, perimeter and area SPI 32L: determine the area of indicated regions involving figures SPI 41A: determine the perimeter & area of 3 or 4 sided plane figuresObjectives:find area of trapezoids, rhombus, and kitesKiteRhombusTrapezoid
2 Area and Perimeter of a Trapezoid A = ½ h(b1 + b2)Height:the perpendicular distance h between the bases.To find Perimeter:add the lengths of the sidesmay need to usePythagorean ThmTriangle ThmTriangle Thm
3 Find the Area of a Trapezoid A car window is shaped like the trapezoid shown. Find the area of the window.A = h(b1 + b2) Area of a trapezoid12A = (18)( ) Substitute 18 for h, 20 for b1, and 36 for b2.12A = Simplify.The area of the car window is 504 in.2
4 Find the Area of a Trapezoid Find the area of trapezoid ABCD.Draw an altitude from vertex B to DC that divides trapezoid ABCD into a rectangle and a right triangle.Because opposite sides of rectangle ABXD are congruent,DX = 11 ftXC = 16 ft – 11 ft = 5 ft.
5 A = h(b1 + b2) Use the trapezoid area formula. 1 2 (continued)By the Pythagorean Theorem,BX 2 + XC2 = BC2, so BX 2 = 132 – 52 = 144.Taking the square root, BX = 12 ft.A = h(b1 + b2) Use the trapezoid area formula.12A = (12)( ) Substitute 12 for h, 11 for b1, and 16 for b2.12A = Simplify.The area of trapezoid ABCD is 162 ft2.
6 Area and Perimeter of a Rhombus or Kite Area = ½ d1d2d is the diagonalTo find Perimeter:add the lengths of the sides
7 Find the area of kite XYZW. Find the Area of a KiteFind the area of kite XYZW.Kite: 2 pairs of adjacent congruent sides.Opposite sides not congruentFind the lengths of the diagonals of kite XYZW.XZ = d1 = = 6 and YW = d2 = = 512A = d1d2 Use the formula for the area of a kite.12A = (6)(5) Substitute 6 for d1 and 5 for d2.A = 15 Simplify.The area of kite XYZW is 15 cm2.
8 Find the Area of a KiteFind the area of rhombus RSTU.To find the area, you need to know the lengths of both diagonals.Draw diagonal SU, and label the intersection of the diagonals point X.
9 … continuedSXT is a right triangle because the diagonals of a rhombus are perpendicular.The diagonals of a rhombus bisect each other, so TX = 12 ft.You can use the Pythagorean triple 5, 12, 13 or the Pythagorean Theoremto conclude that SX = 5 ft.SU = 10 ft because the diagonals of a rhombus bisect each other.A = d1d2 Area of a rhombus12A = (24)(10) Substitute 24 for d1 and 10 for d2.12A = Simplify.The area of rhombus RSTU is 120 ft2.