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 35 feet, with a maximum error in measurement of 1 inch, calculate the area of the end. (Round your answer to two decimal places.) ft2 Use differentials to estimate the maximum error in the calculation of the area. (Round your answer to two decimal places.) ft2

Answer 1

Answer:

The area of the end is 1755.44 ft²

Therefore, the maximum error in calculating area of the end is 8.3592

Step-by-step explanation:

Consider the provided information.

The length of the base is measured to be 35 feet, with a maximum error in measurement of 1 inch,

$1\ inch = \frac{1}{12}\ feet$

The area of shape = Area of square + Area of equilateral triangle

$A=x^2+\frac{\sqrt{3}}{4}x^2$

Substitute x=35 in above.

$A=(35)^2+\frac{\sqrt{3}}{2}\times (35)^2=1755.44$

Hence, the area of the end is 1755.44 ft²

Differentiate $A=x^2(1+\frac{\sqrt{3}}{4})$ with respect to x as shown:

$dA=2x\ dx(1+\frac{\sqrt{3}}{4})$

Substitute dx =1/12 and x=35

$dA=2(35)\ \frac{1}{12}(1+\frac{\sqrt{3}}{4})=8.3592$

Therefore, the maximum error in calculating area of the end is 8.3592