Area of a Kite and a Rhombus

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Presentation transcript:

Area of a Kite and a Rhombus 6.3.1.2 Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.

I can… Determine the area of a rhombus and a kite Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Kite and Rhombus The formula for the area of a rhombus can be justified using the area of a triangle. A specific case follows. The diagonals divide a rhombus and kite into 4 congruent right triangles. So, the area of the rhombus or a kite is 4 times the area of one of the right triangles. Area of 1 triangle = 1/2bh = ½(3)(4) = 6 Area of 4 triangles = 4(6) = 24 Notice that 1/2d1d2 or ½(6)(8), also equals 24

Area of a RHOMBUS or a KITE Only one formula to know! It’s the same for both! Area = ½ the product of the lengths of the diagonals Area = or PLEASE, PLEASE, PLEASE BE CAREFUL!!! IT IS THE PRODUCT OF THE DIAGONALS, NOT THE SUM!!

Find the area of the kite. A = d1d2 B C D A DB = 10m AC = 17m Find the area of the kite. A kite = ½ (10)(17) = 85m2

Find the Area of a Kite A = d1d2 A kite = ½ (7)(6) = 21units2 AB = 2 + 5 = 7 CD = 3 + 3 = 6 2 3 3 A = d1d2 5 A kite = ½ (7)(6) = 21units2

Find the Area of a Rhombus 12 +12 = 24 12 + 12 = 24 A = d1d2 12 m A rhombus = ½ (24)(24) = 288m2

Your Turn… A = d1d2 A kite = ½ (12)(9) = 54units2 AB = 4.5 + 4.5 = 9 CD = 10 + 2 = 12 4.5 2 10 A = d1d2 A kite = ½ (12)(9) = 54units2

Your Turn… A = d1d2 A rhombus = ½ (24)(52) = 624 units2 12 + 12 = 24 26 + 26 = 52 A = d1d2 A rhombus = ½ (24)(52) = 624 units2

I can… Determine the area of a rhombus and a kite Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

A = ½ d1•d2 Area of a Rhombus and a Kite 10.2 Notes Determine the length of the diagonals Copy the equation (don’t just solve in your head) Substitute the numbers for the variables Solve