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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 #5 #, its base has sides of length #1 #, and its base has a corner with an angle of # pi/4 #. What is the pyramid's surface area?

Answer 1

T S A is 20.8067

AB = BC = CD = DA = a = 1
Height OE = h = 5
OF = a/2 = 1/2 = 0.5
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(5^2+0.5^2) = color(red)(5.0249)#

Area of #DCE = (1/2)*a*EF = (1/2)*1*5.0249 = color(red)(5.0249)#
Lateral surface area #= 4*Delta DCE = 4*5.0249 = color(blue)(20.0996)#

#/_C = pi - (3pi)/4 = (pi)/4#
Area of base ABCD #= a* a * sin /_C = 1^2 sin (pi/4) = 0.7071#

T S A #= Lateral surface area + Base area#
T S A # =20.0996 + 0.7071 = color(purple)(20.8067)#

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Answer 2

Sadie Adams

The surface area of the pyramid is ( 5 + 4\sqrt{2} ) square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.