Question

question 11 (mandatory) (1 point)
what is the area of square c?
35 cm
28 cm
a) 2009 cm²
b) 1960 cm²
c) 3969 cm²
d) 90 cm²

Explanation:

Step1: Recall the Pythagorean theorem for areas of squares

If the side - lengths of squares A, B, and C are \(a\), \(b\), and \(c\) respectively, and the right - triangle formed by the sides of the squares satisfies \(a^{2}+b^{2}=c^{2}\). The area of a square is \(A = s^{2}\), where \(s\) is the side - length. So the area of square C is the sum of the areas of square A and square B.
The area of square A with side - length \(a = 35\) cm is \(A_{A}=35^{2}=35\times35 = 1225\) \(cm^{2}\).
The area of square B with side - length \(b = 28\) cm is \(A_{B}=28^{2}=28\times28 = 784\) \(cm^{2}\).

Step2: Calculate the area of square C

\(A_{C}=A_{A}+A_{B}\).
\(A_{C}=1225 + 784=2009\) \(cm^{2}\).

Answer:

A. \(2009\ cm^{2}\)