The figure below shows the first floor plan of a museum. The plan is drawn to scale with 1 centimeter : 0.8 meters. What is the area of the actual museum’s first floor?

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

                   ha = 7*0.8 , ha =  5.6 m

                    1 cm ( drawing ) > 0.8 m ( actual )

                    bs = 18 cm  > ba

                   ba = 18*0.8 , ba =  14.4 m

- 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

                   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

- 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

- 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

The total area ( A ) of the first floor is 375.2 m^2

answer

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step-by-step explanation: