Answer:
The total area ( A ) of the first floor is 375.2 m^2
Step-by-step explanation:
Solution:-
- The architect used a scale of:
1 cm ( drawing ) -----> 0.8 m ( actual ).
- The drawing of the first floor plan of the museum can be broken down into 3 section: A triangle, rectangle and a semi-circle.
- We will determine the area of each section in actual values using the scale of the drawing.
Triangle:-
- The drawing shows a triangle with scale height " hs " = 7 cm and scale base length " bs " = 18 cm.
- First step is to determine the equivalent actual dimension of actual height "ha" and actual base length " ba " using the scale: So,
1 cm ( drawing ) -----> 0.8 m ( actual )
hs = 7 cm -------------> ha
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ha = 7*0.8 , ha = 5.6 m
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1 cm ( drawing ) -----> 0.8 m ( actual )
bs = 18 cm -------------> ba
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ba = 18*0.8 , ba = 14.4 m
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- The area of the triangle is given by the formula:
A1 = 0.5*ba*ha
A1 = 0.5*14.4*5.6
A1 = 40.32 m^2
Rectangle:-
- The drawing shows a rectangle with scale length " ls " = 22 cm and scale width " ws " = 18 cm.
- First step is to determine the equivalent actual dimension of actual length "la" and actual base width " wa " using the scale: So,
1 cm ( drawing ) -----> 0.8 m ( actual )
ls = 22 cm -------------> la
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la = 22*0.8 , la = 17.6 m
========================================
1 cm ( drawing ) -----> 0.8 m ( actual )
ws = 18 cm -------------> wa
========================================
wa = 18*0.8 , wa = 14.4 m
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- The area of the rectangle is given by the formula:
A2 = la*wa
A2 = 14.4*17.6
A2 = 253.44 m^2
Semi-circle:-
- The drawing shows a semicircle with scale diameter " ds " = 18 cm
- First step is to determine the equivalent actual diameter of semicircle "da": So,
1 cm ( drawing ) -----> 0.8 m ( actual )
ds = 18 cm -------------> da
========================================
da = 18*0.8 , da = 14.4 m
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- The area of the semicircle is given by the formula:
A3 = π*da^2 / 8
A3 = π*(14.4)^2 / 8
A3 = 81.43008 m^2
- The total area of the first floor in actual is the sum of area of each sections:
A = A1 + A2 + A3
A = 40.32 + 253.44 + 81.43008
A = 375.2 m^2
Answer: The total area ( A ) of the first floor is 375.2 m^2
