Mensuration and Measurement

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Introduction to Mensuration and Measurement

The word mensuration means the act of measuring, which is what we are here to learn today. In fact, mensuration is the most fun part of geometry (unless you’re crazy about trigonometry)!

The Big Idea: Mensuration and Measurement

Let’s break down the basics of measurement into three basic categories:

  1. Measuring length
  2. Measuring weight
  3. Measuring capacity

Once we have the basics down we will move onto more complex measurements like Area and Perimeter. Mensuration is a very visual study so don’t forget to visualize or even draw all your problems if you’re getting a little stuck!

Measuring Length

It’s useful to have a standard for measuring things. It’s easy to see if you’re taller than your friend or not, but by how much exactly? Sure you could say that you’re taller by a head - but everyone has different sized heads! You can see what I mean in the following puzzles. Write ‘S’ for the shorter objects.

In the above examples we can’t really tell what the length difference is between the objects. That is why your geometry box comes with a ruler (or a ‘scale’). The ruler is used to measure length in two units of measurement:

  1. Centimeter (cm.)
  2. Inches (in.)

Much like the ‘number line’ that we discussed in the Integers chapter, the ruler  represents the positive side of the number line, with equal gaps. Each gap represents 1cm or 1 centimeter which is further subdivided by 10 millimeters, for that extra accuracy! Well there you go, you now know the basics of length measurement! Go have fun with it!

Measuring Weight

The weight of an object is an attribute that is tangible or something you can feel. Pick up an apple in your hand and you know will know the approximate weight of apples. Pick up a lemon however, and you will know instinctively that it weighs lighter than an apple. And while they say that we should never compare apples with oranges, what if we did? Would two apples weigh more than two oranges? They are similarly sized! And that is exactly why we need to be able to measure the weight of an object accurately. The popular instrument of weighing objects is a weighing scale. Can you solve the following problem based on the weighing scale diagram?

Just as we had centimeters (cm) and inches (in) for measuring length of objects, we have standard units of measurement for weight as well. The popular units of measuring weight are:

  1. Grams (g)
  2. Kilograms (kg)

Measuring Capacity

Now suppose you need to know how much milkshake is actually there in your mug, then you’re going to need a unit of measurement for ‘capacity’. The capacity of a cup or glass is the ‘volume’ of substance that can contained in that cup or glass. So if you’re the next big chef, you need to know the exact amount of ingredients that you will add to your dish. The popular units of measuring capacity are:

  1. Milliliter (mL)
  2. Liter (L)

1000 mL = 1L
Judging the level of liquids in the jars, you’ll be able to calculate exactly how much water is in these jars:

Now that you have understood the basics of measuring length, weight and capacity, we can now solve the following problems! Yay! For the following length related problems, you will need to measure the length of different objects using a ruler:

Alright now let’s look at some weight problems. The following problems have different sized weights on a weighing scale on one side, and an object on the other side. Since the weighing scales are balanced, it means that the weight of the object is equal to the sum of weight of the metal weights! Add up the weights to write down the weight of the object:

Finally, let’s discuss some problems related to capacity. Match the left column jar with the glasses of different sizes on the right column. If they match, give it a tick, if they don’t match give it a cross:

(Hint: Add the capacities of the small, medium, and tall glasses to calculate the left side of the column)

Measuring Perimeter

Before we jump into what a perimeter is let’s talk about a ‘geoboard’. What is a geoboard? A geoboard is a geometry board that has equally spaced nails driven into it! We then use geobands or rubber bands to figure out geometry puzzles! It’s a lot of fun, and for the following exercise you’ll need one like the one pictured below:

Okay, so now we can move onto the word ‘perimeter’. The perimeter of a shape is the continuous line forming the boundary of a closed geometric figure. In the above image you can clearly see the perimeters in the triangles, square and rectangle represented by the rubber band. Let us learn to measure the perimeter of various geometrical figures on a geoboard:

Easy, isn’t it?

Here are a couple more puzzles for Perimeter:

Measuring Area

Have you ever entered a room and wondered how big the room is? You might have even counted the tiles and come to a number to describe the space in the room. Area simply put, is the space occupied by a shape or figure. Area is not to be confused with capacity, however. Area is a two-dimensional physical property, and refers to a flat surface space. Capacity, however is a three-dimensional physical property, and refers to say, the inside of a container. Area is measured constantly by architects, designers, and generally people who work with spaces. It’s quite an important concept to grasp, so let’s start with the basics:

Okay, but suppose we needed to actually calculate the area of these shapes, then what would we do? Simple. We break it up into squares with a 1 sq unit (cm) measurement. Then we add them up. Full squares are obviously counted, but more than half squares are counted as well, it’s not exact so we are rounding it off as a full square. Less than half squares are too small, so we aren’t counting them, and two half squares make a full square. Now try to solve the problem:

 

Sub Topics

Here are a few links that will take you through the journey that every Cuemath students undertakes in the pursuit of understanding Mensuration and Measurement along with practice worksheets: