Question

Find the area of the kite.

Answer 1

Answer:

72

Step-by-step explanation:

One way to do this is to use the formula  $A=\frac{1}{2}d_1 d_2$  where $d_1$ and $d_2$ are the lengths of the two diagonals.

In the figure, $d_1=12$  and  $d_2=12$  (2 + 10 and 6 + 6).

The area is $\frac{1}{2}(12)(12)=\frac{1}{2}144=72$ square units.

Another way that doesn't depend on learning a formula is to remember that the diagonals of a kite are perpendicular, so the 4 small triangles are right triangles.  Two of the smaller triangles have base =2 and height = 6, so their areas are 1/2(2)(6) = 6.  Double that--there are 2 congruent small triangles--to get an area of 12.

There are two larger right triangles with base =10 and height = 6, so their area are 1/2(10)(6)=30.  There are two of those, so their combined area is 60.

Finally, put the small triangle area and the large triangle area together to get a total of 12 + 60 = 72