Answer:
(328i + 82) / 17
Step-by-step explanation:
`(2i(4+5i)(4-5i))/(4+i)
= (2i(16 - 25i^2)) / (4 + i)
= (2i( 16 + 25) )) / (4 + 1) [Note:- i^2 = -1]
= 82i / (4 + i)
= 82i(4 - i) / (4 + i)(4 - 1)
= 328i + 82 / (16 - i^2)
= (328i + 82) / 17
Answer:
Step-by-step explanation:
We have been given that Sandra knows the Pythagorean identity 
. She is told that 
and 
.
First of all, we will find value of sine theta using the given identity.
Therefore, .
We have the base measurement for the triangles composing the sides. We need their altitude.
Imagine a right triangle with these sides:
(1) from the apex of the pyramid to the point on the base directly underneath it (471 ft);
(2) from the middle of base edge to the point underneath the apex (half of 708 ft = 354 ft);
(3) the hypotenuse, the altitude of a triangular side.
Using the Pythagorean Theorem, we find the hypotenuse to be
√(471^2 + 354^2) = about 589.2 feet
Now we add up the four triangles' areas. Each is base * altitude / 2, so:
4 x 708 x 589.2 / 2
= 2 x 708 x 589.2
= 834,307.2 square feet, the lateral area.
See attachment for math work and answer.
The area of the shaded region is 49.2.
