Answer:
72
Step-by-step explanation:
One way to do this is to use the formula [tex]A=\frac{1}{2}d_1 d_2[/tex] where [tex]d_1[/tex] and [tex]d_2[/tex] are the lengths of the two diagonals.
In the figure, [tex]d_1=12[/tex] and [tex]d_2=12[/tex] (2 + 10 and 6 + 6).
The area is [tex]\frac{1}{2}(12)(12)=\frac{1}{2}144=72[/tex] 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
