How to Find the Area & the Distance of Shapes

The calculation of areas and distances of shapes forms the foundation for many fields. Careers such as engineering, fashion design and architecture all employ the aspect of area and distance calculation in one way or another. Finding the area and distance of a shape only requires basic information. Finding both the area and distance (perimeter) is dependent on whether the shape is regular or irregular.

Things You'll Need

  • Ruler
  • String
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Instructions

  1. Perimeter

    • 1

      Take a ruler and lay it flat on one edge of the shape you want to measure. Align the zero calibration mark on the vertex of the shape.

    • 2

      Position yourself in a way that your eye level is approximately perpendicular to the zero-centimeter mark. This is to make sure the errors caused by parallax are greatly minimized.

    • 3

      Check on the position of the calibration mark, which is directly aligned at the other end of the edge you were measuring. Again, make sure you maintain an orthogonal eye level to the mark. Record the measurement observed.

    • 4

      Repeat the same procedure for the other remaining edges and record the measurements taken.

    • 5

      Add all the recorded measurements of the shape to obtain its distance or perimeter.

    Distance of Irregular Shapes

    • 6

      Tie a knot on the thin string to symbolize your starting point.

    • 7

      Place the knot of the string on one of the vertices of the shape, and align your eye level appropriately. Mark the starting vertex on the shape using a pencil.

    • 8

      Stretch the string along the edge of the irregular shape as long as the line is somehow straight. In case of a curve, hold the string with two of your fingers just before you arrive at the curve.

    • 9

      Release the other hand holding the knot of the string and use it to stretch the string to another vertex just before another curve appears. Repeat this procedure till you eventually go round the irregular shape. Tie another knot at the end point of your measuring.

    • 10

      Take the string on a ruler and place the knot directly on the zero mark. Stretch the string till you arrive at the other knot on the ruler. Check this measurement with your eye level perpendicular to the knot. Record the total value of the length of the string. In case the string is longer than the ruler, record its length till the end of the ruler and tie another knot. Place this knot on the zero mark and stretch the string to the knot, which symbolized the end point. Record the measurement and add it to the previous one to obtain the perimeter.

    Areas of Regular and Irregular Shapes

    • 11

      Use the ruler to draw lines that are parallel to each other and 1 cm apart along the shape at hand.

    • 12

      Draw other lines which 1 cm apart and are perpendicular to the lines you had initially drawn.

    • 13

      Count the number of complete squares measuring 1 cm by 1 cm formed from the perpendicular lines. Record their number

    • 14

      Count the number of incomplete squares on the shape and record the number. Divide this figure by two to obtain the mean figure.

    • 15

      Add the mean figure to the number of complete squares. Since the area of the small squares is one squared centimeter, the number of squares is indeed the area of the shape.

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