A kite has two perpendicular interior
diagonals. One diagonal is 12 cm longer
than the other diagonal. If the sum of two
diagonals is 52. What is the area of the kite?

To find the area of the kite, we need to first determine the lengths of the diagonals. Let's denote the lengths of the diagonals as \(d_1\) and \(d_2\).

Given:
1. One diagonal is 12 cm longer than the other.
2. The sum of the lengths of the diagonals is 52 cm.

We can set up the following equations based on the problem:
\[
d_1 + d_2 = 52
\]
\[
d_1 = d_2 + 12
\]

We can substitute \(d_1\) from the second equation into the first equation:
\[
(d_2 + 12) + d_2 = 52
\]

Combining like terms, we get:
\[
2d_2 + 12 = 52
\]

Subtract 12 from both sides:
\[
2d_2 = 40
\]

Divide by 2:
\[
d_2 = 20
\]

Now, substitute \(d_2\) back into the second equation to find \(d_1\):
\[
d_1 = d_2 + 12 = 20 + 12 = 32
\]

We have the lengths of the diagonals:
\[
d_1 = 32 \, \text{cm}
\]


Learn how to calculate the area of a kite with two perpendicular interior diagonals, where one diagonal is 12 cm longer than the other. This problem involves determining the lengths of the diagonals using geometric concepts and solving equations. Suitable for students in Grades 7-9.

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