Kite Rhombus Trapezoid

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Presentation transcript:

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 figures Objectives: find area of trapezoids, rhombus, and kites Kite Rhombus Trapezoid

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 sides may need to use Pythagorean Thm 30-60-90 Triangle Thm 45-45-90 Triangle Thm

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 trapezoid 1 2 A = (18)(20 + 36) Substitute 18 for h, 20 for b1, and 36 for b2. 1 2 A = 504 Simplify. The area of the car window is 504 in.2

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 ft XC = 16 ft – 11 ft = 5 ft.

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. 1 2 A = (12)(11 + 16) Substitute 12 for h, 11 for b1, and 16 for b2. 1 2 A = 162 Simplify. The area of trapezoid ABCD is 162 ft2.

Area and Perimeter of a Rhombus or Kite Area = ½ d1d2 d is the diagonal To find Perimeter: add the lengths of the sides

Find the area of kite XYZW. Find the Area of a Kite Find the area of kite XYZW. Kite: 2 pairs of adjacent congruent sides. Opposite sides not congruent Find the lengths of the diagonals of kite XYZW. XZ = d1 = 3 + 3 = 6 and YW = d2 = 1 + 4 = 5 1 2 A = d1d2 Use the formula for the area of a kite. 1 2 A = (6)(5) Substitute 6 for d1 and 5 for d2. A = 15 Simplify. The area of kite XYZW is 15 cm2.

Find the Area of a Kite Find 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.

… continued SXT 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 Theorem to conclude that SX = 5 ft. SU = 10 ft because the diagonals of a rhombus bisect each other. A = d1d2 Area of a rhombus 1 2 A = (24)(10) Substitute 24 for d1 and 10 for d2. 1 2 A = 120 Simplify. The area of rhombus RSTU is 120 ft2.