Question

A. Find the perimeter and the area of Central Park in the scale drawing. Round your measurements for the length and the width to the nearest half centimeter to calculate your answers. The perimeter in the scale drawing is __ centimeters. The area in the scale drawing is __ square centimeters. b. Find the actual perimeter and area of Central Park. The actual perimeter is __ meters. The actual area is __ square meters. Also the length of the shape is 12.5 and the width is 2.5 it also shows 1cm:320m.

Answer 1

The perimeter and the area of Central Park are 9600 meters and 3200000 square meters, respectively.

Calculation of the perimeter of a figure with the help of a scale factor

Let suppose that shape of Central Park is a rectangle. The perimeter ($p$), in square meters, and the area ($A$), in square meters, are found using definition of scale factor and rectangle formulae:

Perimeter

$p = \frac{2\cdot (w+l)}{r}$ (1)

Area

$A = \frac{w\cdot l}{r^{2}}$ (2)

Where:

• $r$ - Scale factor, in centimeters per meters.
• $w$ - Width of the figure, in centimeters.
• $l$ - Length of the figure, in centimeters.

If we know that $l = 12.5\,cm$, $w = 2.5\,cm$ and $r = \frac{1\,cm}{320\,m}$, then the perimeter and the area of Central Park are, respectively:

Perimeter

$p = \frac{2\cdot (2.5\,cm+12.5\,cm)}{\frac{1}{320}\,\frac{cm}{m} }$

$p = 9600\,m$

Area

$A = \frac{(12.5\,cm)\cdot (2.5\,cm)}{\left(\frac{1\,cm}{320\,m} \right)^{2}}$

$A = 3200000\,m^{2}$

The perimeter and the area of Central Park are 9600 meters and 3200000 square meters, respectively. $\blacksquare$

Remark

The statement in incomplete and poorly formatted. Correct form is shown below:

Find the perimeter and the area of Central Park in the scale drawing. Round your measurements for the length and the width to the nearest half centimeter to calculate your answers. The length of the shape is 12.5 centimeters and the width is 2.5 centimeters. Scale factor: 1 cm : 320 m.

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