The perimeter of a rectangular photo frame is 62 cm and its diagonal measures 25 cm. What is the area of the frame, in square cm?

From the perimeter, $l+b=31$; from the diagonal, $l^2+b^2=625$. Squaring the first gives $(l+b{)}^2=961=l^2+b^2+2\text{lb}$, so $2\text{lb}=961-625=336$ and the area lb = 168 sq cm. (The sides are 24 cm and 7 cm.) The trap 336 stops at 2lb and forgets to halve; $775=31\times 25$ multiplies the half-perimeter by the diagonal as though they were the sides; 84 halves the answer a second time.