What is the area of the triangle in the given image, if AP=4, BP=5 and CP=3?

Point P is in the interior of the equilateral triangle ABC. If AP = 7, BP = 5, and CP = 6, what is the area of ABC?

A triangle with sides AB = 3, BC = 4, and AC = 5 has an inscribed square PQRS with side QR along the side AC. What is the area of the square?

You would like to maximize the area of an orange square that you fit between the four blue unit squares that lie on a regular grid as shown:

What is the largest area you can achieve? a) Less than 4 b) 4 c) Greater than 4