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 i

Question

Lostsunrise [7]

3 years ago

7

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 i

s 6 square roots of 2 cm the measure of angle ACB is 45° what is the height of AB

Mathematics

1 answer:

Verdich [7] · Answer 1 · 2022-08-12T21:56:50+03:00

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