00:00 Hello, my name is Dorcas Awaye. I will be teaching you mathematics today, and today's topic is Plane Figures.

00:22 At the end of today's teaching, you should know the similarities and differences between the following, between the square, rectangle, triangle, trapezium, circle, parallelogram,

00:35 The pyramids are of a polygon, square, rectangle, triangle, trapezium, parallelogram, and circle.

00:44 You should also be able to calculate the area of plane shapes such as squares, rectangles, and parallelograms, and to be able to calculate the area of real-life plane objects, such as fields,

00:59 Plan shapes. Plan shapes are figures or shapes that are drawn on a flat or plane surface. Any close to dimensional flat figure is regarded as a plane shape.

01:16 They are called two dimensional shapes because they are given in two directions, the length and the breadth.

01:24 They do not have any thickness. A plane figure is made up of straight lines, cut lines, or both. Either total straight lines, or a combination of straight lines and cut lines, or just cut lines, or through.

01:42 Examples include rectangles, triangles, squares, parallelograms, circle, trapezium, rhumbus, and polygons.

01:53 Different plane shapes have different attributes, such as the number of sides and corners. A side is a straight line that makes part of the shape, and the corner is where two sides meet.

02:06 For example, let me give an illustration of a rectangle. So a rectangle is made up of sides, lines, which are sides, and corners.

02:28 So these are sides, and these are corners. So corners are made up of lines. A corner is where two sides meet. At this point we have a corner.

02:47 Identifying plane shapes. Properties of a rectangle. The opposite sides are equal and parallel. It has equal angles. Each angle at 90 degrees. For a rectangle, each angle is at 90 degrees. This is 90 degrees, 90, 90, and 90.

03:07 Opposite sides are equal and parallel. The diagonal lines are equal and bisect each other. That is the bisect each other. It has two lines of symmetry.

03:26 This is a rectangle. The area of a rectangle is length times breadth. The perimeter is two into bracket length plus breadth. For a square, the properties of a square, all sides are equal. The opposite sides are equal and parallel, unlike a rectangle.

03:48 All angles are equal. Each angle is 90 degrees, just like in the case of a rectangle. The diagonal lines bisect each other at the right angle, 90 degrees, and it has four lines of symmetry.

04:03 Triangle classification according to the sides or lengths. So we have different types of triangles. We have the collateral triangle. We have the scaling triangle and the a socialist triangle.

04:15 So we're going to be talking about the collateral triangle first. It is a triangle with equal sides and equal angles. The properties of an equilateral triangle, all sides are equal. It has three lines of symmetry and all angles are equal at 60 degrees.

04:30 For a triangle, the total sum of angles is 180 degrees and then for each of the angles of an equilateral triangle, we have 60 degrees because all angles are the same.

04:43 A socialist triangle is a triangle with two equal sides and equal base angles. Two sides of an isosceles triangle are equal. The third side is not of the same angle or the same length as the remaining two sides.

05:00 Two sides are equal. Base angles are equal and it has one line of symmetry. For the scaling triangle, it has no equal sides. None of the sides are equal. The properties of a scaling triangle are below.

05:15 None of the three sides are equal. None of the three angles are equal and it has no line of symmetry.

05:23 Parallelogram. Properties of a parallelogram. It is a four-sided plane shape just like a rectangle. It is looking like a slanted rectangle. I call it a slanted rectangle at times.

05:38 Opposite sides are equal just like a rectangle. The opposite sides of a parallelogram are parallel. Opposite angles are also equal.

05:52 The properties of a trapezium are below. It has one pair of parallel sides. The parallel sides are not equal.

06:01 The area is of the sum multiplied by the sum of the parallel sides multiplied by the distance between the parallel sides. The perimeter of a trapezium is the sum of all sides.

06:18 A circle is a round shape without sides or corners. It is not made with lines. So when the lines meet, it doesn't form a corner. It is made of curved lines. That is why it does not have corners.

06:34 Part of a circle, we have the circumference. The arc, the diameter, the radius. Illustrating the circumference, which is known as the distance around the circle, it is illustrated with the red line over there.

06:52 The arc is a portion of a circumference. I'll illustrate that now. If you have a circle, the circumference runs through like this. Any part from here to here can be regarded as an arc. Any part here can be called the arc. Any part of the circumference can be regarded as an arc.

07:18 It is a portion of the circumference. It can be longer and it can be short.

07:27 The diameter is a line that divides the circle into two equal parts and it also passes through the center. So we have a circle and a line that divides it into two equal parts, passing through the center.

07:42 Let's say this is our center. So this is, this line is the diameter. It divides the circle into two equal parts.

07:54 The radius is the line from the center of the circle to the circumference. So from the center of the circle to the circumference, to the circumference, all of these can be regarded as the radius already.

08:11 Properties of the circle before I move there. So a combination of two, the diameter is a combination of radius. So half of the diameter gives you the radius.

08:28 So radius can be calculated as radius can be calculated as diameter divided by two. So you can have your radius this way.

08:47 Properties of a circle, it has infinite number of lines of symmetry. Area of a circle is pi r square, where pi is 3.142 or 22 over 7.

09:00 And r is the radius. Second circumference of a circle is 2 pi r.

09:07 Similarities and differences between squares and rectangles. For similarities they are both called the lateral, that is they both have four sides and four corners.

09:20 They are four interior angles equal 90 degrees and opposite sides are parallel to each other. Differences include, for a square, all sides are of equal length, only the opposite sides are of equal length for a rectangle.

09:38 For the square diagonals of a square are the perpendicular by sector of each other, while the diagonals of a rectangle are not perpendicular by sector of each other.

09:49 For a square, the area of a square is side raised to power of 2. For a rectangle, the area of a rectangle is length times breadth.

09:58 The perimeter of a square is 4 times the side of the length. The perimeter of a rectangle is 2 into bracket length plus breadth.

10:08 We have worked examples here, calculate the perimeter of a football field, which measures 60 meters by 30 meters. From the example, it is noticeable, or you should know that it is not a square field.

10:22 It is a rectangular field, because the dimensions are not the same. We have 60 by 30, so it shows that the length is 60 and the breadth is 30.

10:32 For example, if you had 60 by 60 or 30 by 30, then you know that you are talking about a square-based or square-shaped football field.

10:41 The solution here is to find the perimeter of the field, which is 2 into bracket length plus breadth, 2 into bracket 60 plus 30, which is 90 and 2 times 90 is 180 meters.

10:55 Therefore, the perimeter of the field is 180 meters. Moving on to the second question. A rectangle has a perimeter of 80 meters. Find the length of the rectangle if its breadth is 18 meters.

11:11 From the question you see, we have been given the perimeter, which is 80 meters, and we know the breadth, which is 18 meters. We are left to find the length of the rectangle.

11:21 Like you know, for a rectangle, it has two dimensions, which is length and breadth. We have been given one of the dimensions, which is 18 meters. That is the breadth.

11:30 So we are here to look for the length. And to solve that, since we have been given the value of the perimeter, which is 80 meters, and we already know our formula, which is 2 into bracket length plus breadth.

11:42 So we just impute, substitute our values into the equation.

11:48 Therefore, 80 is into bracket 2. It is equal to 2 bracket length plus breadth, which is 18. To solve that, we divide both sides by 2 to eliminate 2 on the other side, which is 40, equals L plus 18.

12:04 To find the value of L, 40 minus 18 gives you 22 meters. So the length of the rectangle is 22 meters.

12:14 Calculate the circumference of a circle of radius 3 and a half meters. Let's pi by 3 of a 3 raised to power 1 of a 7.

12:23 Solution. The circumference of a circle, as we know, is 2 pi r. And our radius is 3 and a half meters.

12:31 The circumference of a circle, which is 2 pi r, so we have 2 times 3.3 raised to 3, 1 of a 7 times 3 and a half, equals 2 times 22 of a 7 equals 7 of a 2, which is 2 times 11.

12:47 And we have 22 meters. So the circumference of the circle is 22 meters.

12:54 This is your work to do. A rectangle has a parameter of 74 meters. Find the length of the rectangle if its breadth is 17 meters.

13:03 This is just like the example we treated before. You should be able to solve this.

13:08 Calculate the area of a rectangle, which is 6 centimeters by 3.5 cm. Calculate the area of a parallelogram if its base is 9.2 centimeters and its height is 6 centimeters.

13:22 An assembly area is in the shape of a 30 meters by 30 meters square. Part of the area is a concrete rectangle, 25 meters by 5 meters.

13:33 The rest is grass. Calculate the area of the grass. This is a little tricky, but I believe you should understand it.

13:41 Just solve for each of the squares and then you subtract one from the other. You get your answer.

13:47 Thank you for watching. My name is Doka Sawae. Till next time.