Dear children , We have travelled much in the world of mathematics.lets continue our explorations and findings.we have much more to go ahead.lets continue our search.
Can you identify the figure ?
Now draw a diagonal on the figure.
What happened to the parallelogram when a diagonal is drawn? Now the parallelogram split into two triangles, isn’t it? What can you say about the area of parallelogram?
Area of parallelogram is the sum of areas of the triangles. We have already learned about the areas of triangle in class 7. We can compute the area of parallelogram like , The area of parallelogram is the product of one side and perpendicular distance to the opposite side.
What will be the area of the parallelogram?
16 cm
20 cm Area =base x height Base = 20 cm Height = 16 cm Area = 20 x 16 =320 sq.cm
The picture below shows the parallelogram formed by the intersection of two pair of parallel lines. What is the area of the parallelogram? And the perimeter?
3cm 4 cm 2 cm
Can you find the area of this square?
4 cm Area of square =side x side = 4 x4 = 16 sq.cm Can you find its area only when one diagonal length is known?
Area of square is half the square of its diagonal.
6 cm
Can you find its area? How?
Can you identify the figure?
It’s a rhombus .Can you draw the diagonals in the rhombus?
Now cut the rhombus through the diagonal.
What happened to this rhombus now? The rhombus got split into 4 triangles. Now let’s rearrange the picture Which figure did you got?
Now a rectangle is formed. The area of the rhombus will be equal to the area of the rectangle formed. Then what about the length and breadth of the rectangle.
We can see the length of the rectangle is equal to one of the diagonals and breadth is equal to one of the half of length of the second diagonal. Then what will be its area?
Area of rhombus is half the product of diagonals of the rhombus
Compute the area of rhombus?
12 cm 6 cm
Area = (12 x 16)/2 = 36 sq.cm
What is the area of the largest rhombus that can be drawn inside a rectangle of sides 6 cm and 4 cm?
Draw a non-square rhombus of area 9 sq.cm?
What are the properties of this figure?
What is the name of the figure? It’s a trapezium We had already learned its properties.
b
d
a In general let’s take the length of the parallel sides of a trapezium as a, b and the distance between them as d. In the figure Area of upper triangle = (1/2) b d Area of lower triangle = (1/2) a d So the area of trapezium = (1/2) a d + (1/2) b d
Area of trapezium = ½ (a+b) d Find the area of trapezium with parallel sides 6 cm and 8 cm and its perpendicular height is 4 cm. Compute the area trapezium with parallel sides 3 cm and 6 cm and its perpendicular height is 8 cm?
We have already learned different types of quadrilaterals. How can we find its area?
TWA
How many diagonals does this quadrilateral have?
h2 d
h1
We need to know only the distance from the opposite vertices to the diagonals.
Taking the length of the diagonal as d and the perpendicular distance as h1 and h2, the area of the quadrilateral is,
½ dh1 + ½ dh2 = ½ d ( h1 + h2 )
Find the area of the quadrilateral having diagonal 8 cm and length of perpendicular distance from the opposite vertices to the diagonal are 6 cm and 4cm.