1. Area of Rhombus, Kites Objectives: find area of rhombus, and kites

2. of a Rhombus or Kite Area = ½ d 1 d 2 d is the diagonal

3. Find the lengths of the diagonals of kite XYZW. XZ = d 1 = 3 + 3 = 6 and YW = d 2 = 1 + 4 = 5 A = 15Simplify. The area of kite XYZW is 15 cm 2. A = d 1 d 2 Use the formula for the area of a kite. 1212 A = (6)(5)Substitute 6 for d 1 and 5 for d 2. 1212 Find the area of kite XYZW. Find the Area of a Kite Kite: 2 pairs of adjacent congruent sides. Opposite sides not congruent

4. Example 3: Find the Area of the following Kite. 3m 4m 5m A = ½ d 1 d 2 = ½ (6m)(9m) =27m 2

5. Example 4: Find the area of the following rhombus 12m b A = ½ d 1 d 2 = ½ (24m)(18m) = 216m 2 d 1 = 24m d 2 = 18m a 2 + b 2 = c 2 12 2 + b 2 = 15 2 144 + b 2 = 225 b 2 = 81 b = 9 15m

6. Find the area of rhombus RSTU. Draw diagonal SU, and label the intersection of the diagonals point X. Find the Area of a Kite To find the area, you need to know the lengths of both diagonals.

7. 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 = 120Simplify. The area of rhombus RSTU is 120 ft 2. A = d 1 d 2 Area of a rhombus 1212 A = (24)(10)Substitute 24 for d 1 and 10 for d 2. 1212 SXT is a right triangle because the diagonals of a rhombus are perpendicular. … continued

8. Find the area of each figure. Leave your answer in simplest radical form.