Question

The area of the base of the oblique pentagonal pyramid is 50 cm^2 and the distance from the apex to the center of the pentagon is 6 square roots of 2 cm the measure of angle ACB is 45° what is the height of AB

Answer 1

The height, AB, is 6 cm.

The volume of the pyramid is 100 cm3.

Explanation:

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Answer 2

the complete question in the attached figure

Part a)
we know that
ABC is a right triangle
∠ACB=45°
AC=hypotenuse------> 6√2 cm
sin 45=AB/AC-----> AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm

the answer part a) is
AB=6 cm

Part b)
we know that
volume of the pyramid=(1/3)*Area of the base*height
area of the base=50 cm²
height=6 cm
so
volume of the pyramid=(1/3)*50*6----> 100 cm³

the answer part b) is
100 cm³