PLEASE ANSWER THESE TWO GEOMETRY QUESTIONS ASAP FOR ME PLEASE!!
1 answer:
Answer:
~101.5 (area of the shaded area in upper figure)
and
~54.4 (area of the shaded area in lower figure)
Step-by-step explanation:
I attached an image for clarification (please see).
The same approach can be applied to solve these two problems.
As seen in attached image, the shaded area of the 1st figure is the sum of the area of a regular triangle and 3 equal portions.
The area of the regular triangle with side = 12 is:
A1 = side^2 x sqrt(3)/4 = 12^2 x sqrt(3)/4 = 36sqrt(3)
The area of the regular triangle + the area of a portion is:
A2 = pi x radius^2 x (pi/3)/(2pi) = pi x 12^2 x (1/6) = 24pi
=> The area of a porition is:
A3 = A2 - A1 = 24pi - 36sqrt(3)
=> Area of the shade area:
A4 = A1 + 3 x A3 = 36sqrt(3) + 3 x (24pi - 36sqrt(3)) = ~101.5
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For the second figure, the shaded area could be divided into 6 equal parts, each part is inside a regular triangle and is calculated by:
A = the area of the regular triangle - the area of 2 equal portions (white color).
The area of the regular triangle with side = 6 is:
A1 = side^2 x sqrt(3)/4 = 6^2 x sqrt(3)/4 = 9sqrt(3)
The area of the regular triangle + the area of a portion is:
A2 = pi x radius^2 x (pi/3)/(2pi) = pi x 6^2 x (1/6) = 6pi
=> The area of a porition is:
A3 = A2 - A1 = 6pi - 9sqrt(3)
=> Area of a part (including the regular triangle and excluding 2 equal portions):
A4 = A1 - 2 x A3 = 9sqrt(3) - 2 x (6pi - 9sqrt(3))
=> Area of shaded area:
A5 = 6 x A4 = 6 x [9sqrt(3) - 2 x (6pi - 9sqrt(3)) ] =~54.4
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