Problem: If the length of a diagonal of a square is a+ba+ba+b, then the area of the square is:
Answer Choices:
A. (a+b)2(a+b)^{2}(a+b)2
B. 12(a+b)2\dfrac{1}{2}(a+b)^{2}21​(a+b)2
C. a2+b2a^{2}+b^{2}a2+b2
D. 12(a2+b2)\dfrac{1}{2}\left(a^{2}+b^{2}\right)21​(a2+b2)
E. none of these Solution:
A=12d2=12(a+b)2A=\dfrac{1}{2} d^{2}=\dfrac{1}{2}(a+b)^{2}A=21​d2=21​(a+b)2.