Question

The end of a house has the shape of a square surmounted by an equilateral triangle. if the length of the base is measured to be 33 feet, with a maximum error in measurement of 1 inch, calculate the area of the end. (round your answer to two decimal places.)

Answer 1

Answer:

1560.55 ft

Step-by-step explanation:

Both the sides of equilateral triangle and square are represented by x as shown in the sketch (attached). The height of equilateral triangle will be given by

$h=\sqrt {x^{2}-(0.5x)^{2}}=\sqrt {0.75x^{2}}=\sqrt {\frac {3}{4}}=\frac {\sqrt {3}}{2}x$

Area of rectangle=$0.5*x*\frac {\sqrt {3}}{2}x=\frac {\sqrt {3}}{4}x^{2}$

Area of square=x*x=x^{2}

Total area is $x^{2}+\frac {\sqrt {3}}{4}x^{2}$

Total area is $x^{2}(1+\frac {\sqrt {3}}{4})$ and substituting x with 33 ft we obtain

$Area=(33)^{2}(1+\frac {\sqrt {3}}{4})\approx 1560.55 ft^{2}$