Question

The deck of a ship is 35m long. At equal intervals of 5m the width is given by the following table: Width (m) 0 2.9 5.1 6.5 5.9 4.1 3.0 2.3 Estimate the area of the deck.

Answer 1

We will use the Simpson's Rule for areas to solve this question.

The formula to be used here will be:

$A=\frac{i}{3}[(a_1+a_8)+4(a_2+a_4+a_6)+2(a_3+a_5+a_7)]$...Equation 1

Where A is the area to be found, "i" is the interval, the a's are the terms or values of the widths given in the question.

Applying Equation 1 we will get:

$A=\frac{5}{3}[(0+2.3)+4(2.8+6.5+4.1)+2(5.2+5.8+3)]$

Solving the above we get:

$A=\frac{5}{3}[2.3+53.6+28]=\frac{5}{3}\times 83.9\approx139.83$

Thus, the approximate required area is 139.83 squared meters

Answer 2

A =i/3 [(a₁ + a₈) + 4(a₂ +a₄ + a₆) + 2 (a₃ + a₅ + a₇)] This will be our equation 1

Here A is the area we are trying to find.

I is the interval

And a is the values of the width

And when we apply the equation 1 we will get:

A = 5/3 [(0 + 2.3) + 4 (2.8 + 6.5 + 4.1) + 2(5.2 + 5.8 + 3)]

So when we solve this equation we will get this:

A = 5/3 [2.3 + 53.6 + 28]

= 5/3 x 83.9 ≈ 139.83

So the required area is 139.83

Note: We used the Simpson's Rule in this question.