Answer:the value of B is approximately 58.09 cm²
We know that the formula for the volume of a pyramid is given by:
V = (1/3)×B×h
where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this problem, we are given the volume V = 252 cm³, the height h = 12 cm, and one edge of the base a = 7 cm. We need to find the value of B.
Since the base of the pyramid is a right rectangle, we can use the Pythagorean theorem to find the other edge of the base b:
a² + b² = c², where c is the slant height of the pyramid.
c² = h² + ((a/2)²) = 144 + 12.25 = 156.25
c = √(156.25) = 12.5 cm
Now, we can find the area of the base B using the formula:
B = (1/2)×a×b
B = (1/2)×7×√(c² - (a/2)²)
B = (1/2)×7×√(156.25 - 12.25)
B = 21×√(14)