Question

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is `9`, its base has sides of length `6`, and its base has a corner with an angle of `pi/4`. What is the pyramid's surface area?

Answer 1

T S A = 139.2936

Explanation:

AB = BC = CD = DA = a = 6
Height OE = h = 9
OF = a/2 = 6/2 = 103
`EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(9^2+3^2) = color(red)(9.4868)`

Area of `DCE = (1/2)*a*EF = (1/2)*6*9.4868 = color(red)(28.4604)`
Lateral surface area `= 4*Delta DCE = 4*28.4604 = color(blue)(113.8416)`

`/_C = (pi)/4`
Area of base ABCD `= a* a * sin /_C = 6^2 sin (pi/4) = 25.452`

T S A `= Lateral surface area + Base area`
T S A `=113.8416 + 25.452 = color(purple)(139.2936)`