Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.
What is the area of kite ABDC?
Formular for the area of a kite is expressed as;
A = pq/2
Where p and q are the two diagonals of the kite.
Given the data in the question;
- Diagonal p = line BC = BM + MC = 3 + 3 = 6
- Diagonal q = line AD = AM + MD
- Line AM = ?
- Line MD = ?
From the diagram, we can determine line AM and line MD using Pythagoras theorem.
c² = a² + b²
First, we find line AM
c² = a² + b²
5² = 3² + b²
25 = 9 + b²
b² = 25 - 9
b² = 16
b = √16
b = 4
Line AM = 4
Next, we determine Line MD
c² = a² + b²
(√58)² = 3² + b²
58 = 9 = b²
b² = 58 - 9
b² = 49
b = √49
b = 7
Line MD = 7
Now, we can find the area of the kite.
Diagonal p = BC = 6
Diagonal q = AD = AM + MD = 4 + 7 = 11
Area = pq/2
Area = [ 6 × 11 ]/2
Area = 66 / 2
Area = 33cm²
Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.
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