GCSE Maths - How to find the Area of Compound Shapes #106
Summary
TLDRThis educational video teaches viewers how to calculate the area of irregular shapes by breaking them down into simpler geometric figures like rectangles, triangles, parallelograms, and trapeziums. The script illustrates the process with examples, showing how to find areas by using basic formulas for these shapes. It guides through calculating the area of a rectangle and a triangle combined, and then a rectangle and a trapezium, highlighting the importance of understanding how to decompose complex shapes into manageable parts for area calculation.
Takeaways
- 📏 To find the area of irregular shapes, they must be divided into smaller, recognizable shapes like rectangles, parallelograms, triangles, and trapeziums.
- 🔢 The formulas for calculating areas of simple shapes are essential: length x width for rectangles, base x height / 2 for triangles, and (a + b) / 2 x height for trapeziums.
- 🔍 For composite shapes, identify and calculate the area of each simple shape component and then sum them to get the total area.
- 📐 When a shape includes a triangle, calculate its height if not given by subtracting the height of any included rectangles from the total height.
- 📈 The example in the script demonstrates how to decompose a shape into a rectangle and a triangle, calculate their areas separately, and then add them to find the total area.
- 📉 Another example shows how to handle a shape with a trapezium on top by first calculating the area of the rectangle and then the trapezium using the average of the parallel sides.
- 📝 The script emphasizes the importance of understanding how to break down complex shapes into simple ones for area calculation.
- 🎯 The video provides a practical approach to solving area problems by visually demonstrating the process with specific examples.
- 💡 The tips shared are useful for students or anyone needing to calculate areas of irregular shapes for mathematical, architectural, or artistic purposes.
- 📚 The video encourages viewers to visit a live past paper website for additional educational resources, enhancing learning opportunities.
Q & A
What is the main challenge when calculating the area of irregular shapes?
-The main challenge is that irregular shapes don't have their own formulas like rectangles or triangles do, so they need to be divided into smaller, familiar shapes to calculate their areas.
What are the four basic shapes whose area formulas we need to know for this process?
-The four basic shapes are rectangles, parallelograms, triangles, and trapeziums, as they have known area formulas.
How can you split a complex shape into simpler shapes to calculate its area?
-You can split a complex shape by drawing lines to create rectangles, triangles, trapeziums, or parallelograms, whose areas can be calculated using known formulas.
What is the formula for the area of a rectangle?
-The formula for the area of a rectangle is length times width.
How do you calculate the area of a triangle?
-The area of a triangle is calculated using the formula one half times base times height.
In the example given, why is the height of the triangle 3 centimeters?
-The height of the triangle is 3 centimeters because the total height of the shape is 7 centimeters, and the rectangle at the bottom takes up 4 centimeters of that height.
How do you find the total area of a compound shape after calculating the areas of its parts?
-You find the total area of a compound shape by adding together the areas of each of its simpler shapes.
What is the area of the rectangle in the second example of the script?
-The area of the rectangle in the second example is 180 square centimeters, calculated by multiplying the length (15 cm) by the width (12 cm).
How is the area of a trapezium calculated according to the script?
-The area of a trapezium is calculated by finding the average of the two parallel sides (a + b)/2 and then multiplying by the height.
In the script, what is the total area of the second compound shape after breaking it down into a rectangle and a trapezium?
-The total area of the second compound shape is 205 square centimeters, which is the sum of the rectangle's area (180 cm²) and the trapezium's area (25 cm²).
What additional resource is mentioned at the end of the script for further practice?
-At the end of the script, a live past paper website is mentioned where viewers can practice similar problems.
Outlines
📏 Finding Areas of Complex Shapes
This video segment introduces a method for calculating the area of irregular shapes by breaking them down into simpler, familiar geometric shapes like rectangles, parallelograms, triangles, and trapeziums. The segment emphasizes the importance of knowing the area formulas for these basic shapes and demonstrates how to decompose a complex shape into a rectangle and a triangle. The process involves identifying the dimensions of the simpler shapes, calculating their areas using the respective formulas, and summing these areas to find the total area of the complex shape. An example is given where a shape is divided into a rectangle (5 cm by 4 cm) and a triangle (base 5 cm, height 3 cm), and their areas are calculated and added to get a total area of 27.5 square centimeters.
Mindmap
Keywords
💡Area
💡Shapes
💡Rectangle
💡Triangle
💡Formulas
💡Parallelogram
💡Trapezium
💡Compound Shapes
💡Measurements
💡Horizontal Line
💡Calculation
Highlights
Introduction to finding the area of complex shapes without direct formulas.
Explanation of breaking down complex shapes into simple shapes with known area formulas.
Recap of the main formulas for rectangles, parallelograms, triangles, and trapeziums.
Terminology distinction between simple and compound shapes.
Step-by-step demonstration of dividing a shape into a rectangle and a triangle.
Calculation of the rectangle's area using length and width.
Determination of the triangle's height by subtracting the rectangle's height from the total height.
Use of the triangle area formula with calculated base and height.
Summation of areas to find the total area of the compound shape.
Approach to simplifying complex shapes by cutting off protruding parts.
Calculation of a rectangle's area with a new set of dimensions.
Explanation of finding the average length for a trapezium's area calculation.
Application of the trapezium area formula using the average length and height.
Final calculation of the total area by adding the rectangle and trapezium areas.
Encouragement to visit a live past paper website for further resources.
Conclusion of the video with a summary of the key points covered.
Transcripts
[Music]
in today's video we're going to cover
how you can find the area of strange
looking shapes like these three
the problem with shapes like these is
they don't have their own formulas like
rectangles or triangles do
and so to find their areas we instead
have to split them up into smaller
shapes that we do know the formulas for
to quickly recap the main formulas you
need to know are these four here
which are the ones for rectangles
parallelograms
triangles and trapeziums
so when you're given a weird shape the
aim is to break it up into some
combination of these four shapes that we
know the formulas for
and one thing to point out is that we
sometimes call these four easy shapes
simple shapes because we have formulas
for them
whereas the more complicated shapes that
we're focusing on in this video are
often called compound or composite
shapes
because they're made up of two or more
simple shapes
let's start with this one in the middle
and add some measurements so that we can
work through it
the first thing to spot here is that if
we draw a horizontal line across the top
here
then we can split this shape into a
rectangle at the bottom and a triangle
at the top
so then all we need to do is find the
area of each of them and add the two
together
so to find the area of this rectangle we
need to use this formula in the top left
as do length times width
which in our case would be the length of
5 centimeters
times the width of four centimeters
which gives us 20 square centimeters
then to find the area of the triangle at
the top we need to use this formula of
one half times base times height
the base will just be five centimeters
because it's the same length as this
base of the overall shape
however we haven't actually been told
the height of the triangle so we're
gonna have to work that out for
ourselves
what we do know is that the height of
the entire shape is seven centimeters
and the rectangle makes up four
centimeters of that
so the height of the triangle must just
be the difference between four
centimeters and seven centimeters
which we can find by doing seven minus
four to get three centimeters
and now that we have our dimensions we
can find the area by just doing one half
times the base of five times the height
of 3 and we get 7.5 square centimeters
and then to finish the question we work
out the total area of the shape by
adding together the areas of our
rectangle and our triangle so 20 plus
7.5
which is 27.5 square centimeters
and that's our answer
if you look at this next one
you can see that this bit at the top is
sort of sticking out a bit
and so to make it easier for ourselves
we can just cut that bit off with a
horizontal line along here
and we're now left with a big rectangle
at the bottom
and a small trapezium on top
to find the area of the rectangle we
just do a length times width again
so 15 times 12
which is 180 centimeters squared
next if you look at the formula for
trapeziums in the bottom left
we first have to find the average length
by doing a plus b over two and then
multiply that by the height
and remember a and b in this formula are
just the top and bottom lengths of the
trapezium
so in our case we'll do four plus six
all over two
and then times that by the height of
five
and if we simplify that the four plus
six is ten
and then the ten divided by two is just
five so we have five times five which is
25 centimeters squared
then to finish we just add together the
areas of the rectangle and the trapezium
so 180 plus 25
to get a total area of 205 centimeters
squared
anyway that's everything for this video
so hope it was helpful
if you haven't seen it already we now
have a live past paper website up so you
can just click this button in the top
right corner of this screen and you can
check out our new website
hope you enjoy
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