Measuring Irregular Areas with Graph Paper

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16 Questions

If the enclosed region has a regular geometric shape, we can use standard formulae to find its ______.

area

Then we need to use a ______ paper.

graph

To find the area enclosed by the outline, count the number of squares inside it. Count a square only if half or more of it lies inside the ______.

outline

The total number of squares, multiplied by the area of each square, gives the area inside the ______.

outline

The thicker lines on the ______ paper are 1 cm apart, while the thinner lines are 1 mm apart. Thus, the entire paper is divided into small squares of area 1 mm² each, and larger squares of area 1 cm² each.

graph

For the shape in Figure 1.1, the number of squares with half or more within the ______ = 7.

outline

The total number of squares = 17...the area of each large square = 1cm², the area of the irregular shape = 17 x 1 cm² = ______ cm².

17

Place a piece of paper or cardboard with an irregular shape on a graph paper and draw its ______.

outline

The unit of volume is given by the cube of the unit of ______.

length

If length is measured in cm, the unit of volume is ______.

cm³

The litre symbol is represented by the letter ______.

L

Containers with a fixed capacity are used for measuring the volume of ______.

liquids

Conical measuring cans are generally used to measure liquids sold by ______.

volume

Metal cups with long handles are commonly used for measuring ______ or cooking oil.

milk

The inner volume or capacity of a container is measured in terms of the liquid it can ______.

hold

The volume of liquid which a container can hold is called its ______.

capacity

Study Notes

Measuring Irregular Areas

  • Area is the measure of the region inside a closed line.
  • To find the area of an irregular shape, use a graph paper with parallel lines (thicker lines 1 cm apart, thinner lines 1 mm apart) to divide the paper into small squares (1 mm² each) and larger squares (1 cm² each).
  • Count the number of squares inside the outline, counting only those with half or more of the square inside the outline.
  • The total number of squares, multiplied by the area of each square, gives the area inside the outline.

Measuring Volume

  • The unit of volume is given by the cube of the unit of length (e.g., meter³, cm³, etc.).
  • The litre (L) and millilitre (mL) are units of volume used to measure the volume of liquids.
  • 1 m³ = 1,000,000 cm³, 1 L = 1000 cm³, and 1 mL = 1 cm³.
  • Gallon and ounce are units of volume used in the UK and US, but they measure different volumes in the two countries (e.g., 1 US gallon = 3.78 L, 1 UK gallon = 4.54 L, etc.).
  • A hollow body or container has an outer volume and an inner volume (capacity), measured in terms of the liquid it can hold.
  • Containers with fixed capacities, such as conical measuring cans and metal cups, are used to measure the volume of liquids.

Learn how to measure the area of irregular shapes using graph paper. Explore the concept of dividing a region into small squares and calculating the total area by counting the squares. Understand the significance of using graph paper for determining areas of irregular shapes.

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