A scale drawing of a square object has a scale of 1 in. : 5 mm. The scale drawing has a length of 2.5 inches. Find the perimeter and the area of the object in the scale drawing. Then find the perimeter and area of the actual object.

The perimeter of the actual object is 50 mm.

The area of the actual object is 156.25 mm square

Step-by-step explanation:

Given

Shape: Square

Scale: 1 in : 5 mm

Length of Scale Drawing = 2.5 in

Required:

- Perimeter of Actual Object

- Area of Actual Object

Calculating the perimeter of the actual object

Provided that the shape is a square;

The perimeter of the actual object is calculated by

Perimeter = 4 * Length

Recall that the scale is 1 in : 5 mm

This means 1 in on the scale represents 5 mm of the actual measurements of the object.

So, if 1 in ≈ 5 mm, then

2.5 in ≈ 2.5 * 5 mm

2.5 in = 12.5 mm

So, Length = 12.5mm

Now, the perimeter of the actual object can be calculated.

P = 4 * 12.5mm

P = 50mm

Hence, the perimeter of the actual measurements is 50 mm.

Calculating the area of the actual object

The area of the actual object is calculated by

Area = Length * Length

Recall that Length = 12.5 mm as calculated above

So,

Area = 12.5 * 12.5

Area = 156.25 mm square

Hence, the area of the actual object is 156.25 mm square

Perimeter and area of drawing

Perimeter = 10 In

Area = 6.25 In²

Perimeter and area of object

Perimeter = 51.836 mm

Area = 167.936 mm²

Step-by-step explanation:

We are dealing with a square object, so let's talk about the drawing first.

The length of one side = 2.5 In

Perimeter of square = 4L

Perimeter = 4*2.5

Perimeter = 10 In

Area = L*L

Area = 2.5*2.5

Area = 6.25 In²

Letd note that 1 inch =

25.4 millimetres

So 2.5 Inch = 2.5 * 25.4

2.5 In = 63.5 mm.

25.4 mm is to 5mm

63.5 mm is to (63.5*5) / 24.5

63.5mm is to 12.959 mm

So the length of actual object is 12.959mm

The perimeter = 4*12.959

Perimeter = 51.836 mm

Area = 12.959²

Area = 167.936 mm²