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Presentation on Area

Square, Rectangle and Parallelogram

Area is just counting the squares found inside a figure.

There are 4 squares in this figure. It is for this reason that the area in this figure is 4 square units. Area is counting the squares found inside the figure.

There are 36 squares in this figure. Let’s try this! Remember: Area is counting the squares found inside the figure. It is for this reason that the area of this figure is 36 square units.

Now, formulas are created so we don’t get tired counting the squares. Area = base x height Base Height Area = 2 x 2 Area = 4 Square Units Base Height Area = 9 x 4 Area = 36 Square Units Side = 2 = 9 = 4 Length Width

Now, it will be easier to see that if we turn this parallelogram into a rectangle! A = b x h A = 6 x 4 A = 24 square units

We have turned the parallelogram into a rectangle. Now, it is clear that the area is 24 square units.

Try solving the area of the following!

10 cm 15 cm 8 4 ft 5 ft 12 ft Area = 64 square units Area = 150 square cm Area = 48 square ft. Area = 12 square units

Good job!!! Let’s go to the next!!!

Triangle and Trapezoid

Now, let us derive the formula for the area of a triangle based on the area of this rectangle. Area = base x height 2

It is for this reason that the area of a triangle is b x h 2 A triangle is always half of a parallelogram. By the way, a rectangle is a parallelogram!

Try solving the area of the following!

12 7 Area = 42 square units 9 6 Area = 27 square units 3 cm 5 cm Area = 7.5 square cm Area = 55 square in 10 in 11 in

Did you know that a trapezoid has the same formula as that of a triangle? Watch this!!! Area = base x height 2

The only problem we have is that in a trapezoid, there are 2 bases. Area Base 1 Base 2 = xheight Base So, the whole base, is actually the sum of base 1 and base 2. + Height 2 base(b 1 + b 2 ) Base 1

Try solving the area of the following!

Area = 15 square units Area = 21 square yd Area = 18 square ft Area = 9 square units yd 10 yd 4 yd 2 ft 14 ft 4 ft

You have done a great job! Remember: Area is just counting squares inside a figure!

The Circle

Even for circles, area can be solved by just counting the squares inside it! Some mathematicians would try to approximate the area of a circle by directly counting the squares in it! Watch this!

Let us try to approximate the area of this circle by directly counting the number of squares inside it. Please remember, we are only approximating! approximating!

Count with me! 1 1,, 2 2,, ,,,,, ,,,,, ,,,,, ,,,,, ,,,

So, there are about 28 squares in here. So, the area of this circle is approximately 28 square units! That was too much work! Now, let us apply the formula to shorten our task!

Base Height radius

There about 3 squares with sides equal to the radius, within a circle. Area = r x r x 3.14 or Area = r 2 

Remember that the area of this figure is about 28 sq. units. Let us apply the formula and see if we are close! A = r x r x 3.14 Or A = r 2 

A =3 r r x3.14 x 3 A = 9 x 3.14 A = sq. units Well, we are very close! ≈ 28 sq. units

Now, try this!

Use  = 3 2 Area = 12 square units 3 cm Area = 27 square cm 5 in Area = 75 square in

Well done!!! Now, let’s try this next challenge!!!

Now, use  = Area = 3.14 square units 2 cm Area = square cm 10 in Area = 314 square in

You have done an amazing job! Remember: Area is just counting squares inside a figure and formulas are created to make our life easier! I hope you have learned a lot today! Bye and thank you!!!