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Find the Area of Kites, Rhombuses and Trapezoids

Find the Area of Kites, Rhombuses and Trapezoids. 1. A kite has two diagonals. We’ll label them. 2. The diagonals in a kite make a right angle. 3. Let’s put a rectangle around the kite because we know the formula for the area of a rectangle.

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Find the Area of Kites, Rhombuses and Trapezoids

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  1. Find the Area of Kites, Rhombuses and Trapezoids

  2. 1. A kite has two diagonals. We’ll label them. 2. The diagonals in a kite make a right angle. 3. Let’s put a rectangle around the kite because we know the formula for the area of a rectangle. 4. The diagonals have the same lengths as the sides of the rectangle, so… 5. Fill in the empty space around the kite with a different color. 6. The kite takes up half the space of the entire rectangle, so… Area of kites – Explanation 2 2 1 1 90 Diagonal #1 1 1 Diagonal #2 2 2 Diagonal #2 Area of the Rectangle = (d1)(d2) Diagonal #1 Area of a Kite = ½ (d1)(d2)

  3. Area = ½ (d1)(d2) = ½ (9+35)(12+12) = ½ (44)(24) = 528 square units Find the area of the kite 15 15 9 12 12 35 Be sure to identify the diagonals right away. 37 37

  4. Area = ½ (d1)(d2) = ½ (6+15)(8+8) = ½ (21)(16) = 168 square units Find the area of the kite Be sure to identify the diagonals right away. 10 10 6 8 8 15 Use the Pythagorean Theorem to find the missing pieces of the diagonals 17 17 8 10 6 y 17 x

  5. 1. A Rhombus has two diagonals. Label them. 2. The diagonals make a right angle. 3. Let’s put a rectangle around the rhombus because we know the formula for the area of a rectangle. 4. The diagonals have the same lengths as the sides of the rhombus, so… 5. Fill in the empty space around the rhombus with a different color. 6. The rhombus takes up half the space of the entire rectangle, so… Area of Rhombuses – Explanation 2 2 1 1 Diagonal #1 90 Diagonal #2 1 1 Diagonal #2 2 2 Area of the Rectangle = (d1)(d2) Diagonal #1 Special Note: …because a rhombus is a parallelogram, the formula for parallelograms will sometimes work as well. Area of a Rhombus = ½ (d1)(d2)

  6. Area = ½ (d1)(d2) = ½ (5+5)( + ) = ½ (10)() = square units Find the area of the rhombus 10 10 5 5 10 60 10 Be sure to identify the diagonals right away. Long leg Use the 30-60-90 triangle rules to find the missing pieces of the diagonals 30 Short leg 5 10 60 hypotenuse

  7. 1. A trapezoid has two bases and a height. Let’s label them. 2. Let’s add a third horizontal line through the middle of the figure. 3. Now let’s put a rectangle over the trapezoid. 4. Finally, lets cut off the ends of the trapezoid and move them. 5. This means the trapezoid and the rectangle have the same area. Area = (Avg of Bases) (Height) Area of a trapezoid - explanation Base 2 Avg of Bases Height Base 1 The Area of a Trapezoid = (Avg of Bases) (Height) OR ½ (B1 + B2)(Height)

  8. Area=(Avg of Bases)(Height) =½ (B1 + B2)(Height) =½ (20 + 10)(8) =½ (30)(8) =120 square units Find the Area of the trapezoid Base 2 10 8 20 Base 1 Be sure to identify the bases and the height right away.

  9. Area=(Avg of Bases)(Height) =½ (B1 + B2)(Height) =½ (16 + 4)(Height) =½ (20)(6) = 60 square units Find the Area of the trapezoid Base 2 4 16 - 4 = 12 12 / 2 = 6 h=6 4 6 6 45 16 Base 1 Be sure to identify the bases and the height right away. Use the 45-45-90 triangle rules to find the height 6 We need to find a side on the triangle so we need to break Base 1 into three pieces. Same 45 6

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