It’s time for me to teach you guys another maths topic! How to find the area of shapes is what we are talking about next! How to find the area of different shapes is a maths topic that is sure to appear in your child’s homework from around Primary 5 onwards. Area can be quite tricky at the start, and some questions are more challenging than others. But your child must understand this maths topic as they will be working with area from primary school into secondary school. Unfortunately, there’s no escape from area questions for a while! In this blog post, I will go through how to find the area of different shapes, the types of questions your child may get asked and how area questions may appear in the SEAG transfer test.
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What is the area?
The area of a shape is how much space a shape takes up! When calculating the area of a particular shape, we are measuring the inside of the shape. When students start exploring the area of shapes, they are usually given a selection of shapes that have squares inside them, and they just count how many squares there are. But as they move through primary school, area becomes a bit more difficult and the questions more challenging.
What is the difference between area and perimeter?
Area and perimeter usually come hand in hand in maths. So it can be easy to get these two mathematical concepts jumbled up! The perimeter of a shape is the total distance around the outside of the shape. Whereas the area of a shape is measuring the inside of the shape. To calculate the perimeter of a shape, we add up all the measurements of the outside of the shape. With area, we multiply the height of the shape by the width of the shape, and this tells us what the inside measures.
How to find the area of different shapes
To calculate the area of most 2D shapes, we multiply the height by the width. The units of measurement for area will always have the squared symbol after the metric unit. For example, if the area of a shape is in centimetres, the unit will be cm2.
How to find the area a triangle
Finding the area of a triangle can make an appearance in your child’s Key Stage 2 Maths homework. If your child is sitting the transfer test, it can also show up in some practice papers and revision materials. Finding the area of a triangle can seem a bit daunting at first, but it’s not too bad when you know how. There are a few different types of triangles: right angle, isosceles, equilateral and scalene. If your child is asked how to find the area right triangle, it’s the same method as finding the area of all the other triangles. There isn’t a different method for each type of triangle. There are two ways to find the area of a triangle, your child can choose whichever one they find easiest.
How to you find the area of a triangle – Option 1:
The first way to find the area of a triangle is to half the base and multiply it by the height of the triangle. A time when this can become a bit trickier is if the base of the triangle is an odd number, so when your child halves it, it becomes a decimal number. It’s still manageable, but it just takes a bit more working out sometimes.
How to you find the area of a triangle – Option 2:
The second way to find the area of a triangle is to multiply the base by the height of the triangle and then half your answer. Sometimes, this option works out easier than option 1. As long as your child remembers to half their answer after multiplying.
Area of Compound Shapes
These types of area questions, as the ones that confuse my students, are the beginning. The mathematical term is compound shapes, but I just call them ‘weird’ shapes because sometimes they are really, well, weird! If your child is asked to find the area of a compound shape, there are a couple of steps they will have to take. Let’s go through an example question together.
Step 1: Split or Divide the Shape
Take a look at the compound (or weird) shape that the question is giving you. Then, we need to split or divide the shape into a more manageable shape. Sometimes we can split it into two shapes, or sometimes it will be three or four shapes.
Step 2: Compound Shapes Area
Once your child has split the shape into as many as they need to, they will find the area of each of the shapes separately. When they are doing this, they are just multiplying the height by the width. Sometimes, with these types of questions, your child will have to find some missing lengths. To do this, they will need to use the measurements they have already been given to find the missing measurements. (I will go over this later in this blog post)
Step 3: Add
Once your child has calculated the area of each of the shapes they have divided the main compound shape into, they need to add up all the areas to get a total. And voila! They have just found the area of a compound or ‘weird’ shape!
How to find the missing area
I told you at the beginning of this blog post that the area topic gets more complicated as we go along, didn’t I? Now we are going to find the area when measurements of a shape are missing…I know this is torture, isn’t it! But once again, it’s not too bad with practice! Typical questions where your child will have to do this are with compound shape questions or questions where students are given two shapes with the same area, but one of the shapes has missing measurements. Let’s take a look at an example of each of these questions.
Finding missing lengths in compound shapes:
To find missing lengths in compound shapes, we need to use the measurements that we have already been given. With the L shape below, we are given 4 measurements out of the 6 sides. We can split this shape into two rectangles. To find the missing lengths, we need to use the measurements we have already been given. If we subtract 4cm from the base of the rectangle, which is 12cm, this gives us 8cm, which is the first of our missing measurements. Then we will use the height of the L shape, which is 14cm, and subtract the height of rectangle 1, which is 8cm. This leaves us with 6cm for the height of rectangle 2.
Next, we find the area of rectangle 1 by multiplying 12cm by 8cm. This gives us 96cm2. Then we find the area of rectangle 2 by multiplying 4cm by 6cm, which gives us 24cm2. The last step with this question is to add 96cm2 and 24cm2. This gives us an answer of 120cm2, which is the area of the complete L shape.
Finding the area of shapes with missing measurements:
This type of question comes up in the transfer test and practice papers occasionally. Students are given two shapes which have the same area, but one of the shapes has missing measurements. With the question below, we are given a square and a rectangle. Both shapes have the same area, but Shape B has a missing length, and this is what we are trying to find out. Shape A is a square, which means all of the sides are the same length. To find the area of Shape A, we multiply 8 by 8, which gives us 64cm2. This means the area of Shape B is also 64cm2. We know one of the measurements of Shape B is 4cm. To find the missing length, we divide 64cm by 4cm, which gives us 16cm!
Area Word Problems
Another popular way that your child will have to work with area is completing area word problems. Sometimes, area word problems will also have shapes or graphics to go along with them, and sometimes they don’t; your child will just be given the measurements. Sometimes, my students will be completely fine calculating the area of shapes, but when it’s in a word problem version, they panic. If this happens with your child, just keep calm, and you can even use the measurements from the question to draw out a wee shape for them so they have a visual. Remember, word problems are just mathematical equations with a ‘story’ around them.
Area Transfer Test Questions
There are several ways that area can make an appearance in the transfer test, so your child must be confident and comfortable completing the different types of area questions. The types of area questions that I have seen appear in the transfer tests over the years are:
- Area of 2D shapes
- Area of triangles
- Area of compound shapes
- Area of shapes with missing lengths
- Finding the area when perimeter is given
- Area word problems
I will give you an example of each of these types of questions in the SEAG transfer test style so your child can have a practice of each.
Area of 2D Shapes
The first way that area can appear in the transfer test is simply finding the area of a 2D shape. This will usually be a square or rectangle. To find the area of most shapes we multiply the height by the width. For example, what is the area of the rectangle below?
Area of triangles
Next, we have finding the area of a triangle and remember to find the area of a triangle we either half the base and multiply by the height OR multiply the base by the height and then half your answer. For example, what is the area of the right angle triangle?
Area of compound shapes
This one may take a bit of time to get right, but finding the area of compound shapes can make an appearance in the transfer test. Sometimes, it can be asked in a word problem format. For example, John bought a storage box to keep his garden tools in. Below is a plan of the storage box. What is the area of the storage box?
Area of shapes with missing lengths
Finding the area of shapes with missing lengths can also be a popular transfer test style area question. A top tip is to encourage your child to use the information from the question to find the missing lengths. For example, Shape A and Shape B have the same area. What is the missing length from Shape B?
Finding the area when only the perimeter is given
This can be another tricky type of question: how to find the area when the perimeter is given. Once again, we need to use the information we are given to help us. For example, if we have a rectangle which has a perimeter of 40cm with one of the sides being 5cm, we can use this information to find the area of the rectangle. If two sides of the rectangle total 10cm, we can subtract this from the total perimeter of 40cm. This leaves us with 30cm, which we need to divide between the other two sides of the rectangle. This means the missing lengths are 15cm. To find the area of the rectangle, we multiply 15cm by 5cm, which gives us an area of 75cm2.
Area word problems
Word problems can cause a bit of panic and worry with some students. If this is how your child reacts to word problems, remind them that they’re just a calculation with a ‘story’ around it. For example, Ashleigh is getting a new carpet for her living room. Her living room is rectangular in shape and measures 8m by 12m. How much carpet must Ashleigh buy for her living room? With this question, we are finding the area of a rectangle, there’s just a ‘story’ around this sum.
Another example of an area word problem that can come up in the transfer test is similar to this: Below is a plan of a patio with tiles and a pool. The shaded area is the pool. What is the area of the tiles? With this question, students need to find the area of the whole rectangle and then find the area of the pool. The next step is to subtract the area of the pool from the complete area of the rectangle. This will tell you the area of the tiles.
More information on how to find the area
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How to make your child’s mean mode median and range homework easy and calm
So, that’s all of the ways that I can think of that area can be asked in your child’s maths homework and transfer test preparation. When your child asks how to you find the area, I hope you will be an area whizz! And if not, just come back to this blog post and give yourself a wee refresher on how to find the area!
