Area, Perimeter and Volume of Geometrical Figures
Category : 5th Class
Area, Perimeter and Volume of Geometrical Figures
Perimeter
Perimeter is referred as the length of the boundary line, which surrounds the area occupied by a geometrical shape.
Find the perimeter of the following figure.
Solution:
Perimeter of the figure = 4 cm + 3 cm + 4 cm + 2.5 cm+ 5 cm + cm = 23.50.
Perimeter of the Triangle
A triangle has three sides. Perimeter of a triangle is the sum of its all the three sides.
Perimeter of the triangle ABC = AB + BC + CA
Find the perimeter of the following triangle.
Solution:
Perimeter of the triangle PQR = 4 cm + 4.7 cm + 6 cm= 14.7 cm
Perimeter of the Quadrilateral
Perimeter of a quadrilateral is the sum of the length of its four sides.
In quadrilateral ABCD, perimeter = AB + BC + CD + DA
Find the perimeter of the following quadrilateral.
Solution:
Perimeter of the quadrilateral = 5 cm + 3 cm + 4 cm + 3 cm = 15 cm
Perimeter of Rectangles
Perimeter of a rectangle = 2 (Length + Breadth).
Find the perimeter of the rectangle whose length is 12 cm and breadth is 8 cm.
Solution:
Perimeter of the rectangle = 2 (12 + 8) = 40 cm.
Perimeter of Squares
Perimeter of a square = 4 \[\times \]side.
Perimeter of the square ABCD = 4 \[\times \]AB
Find the perimeter of the square whose length of one side is 9 cm.
Solution:
Perimeter of a square = \[4\,\,\times \,\,9\]cm = 36 cm
Perimeter of a Circle
Perimeter of a circle = \[2\pi r\]
Where \[\pi \]\[=\,\frac{22}{7}\] = 3.14 and r = radius of the circle
If radius of a circle is 0.35 cm, find the perimeter of the circle.
Solution:
Perimeter the circle\[=\,\,2\,\,\times \,\,\frac{22}{7}\,\,\times \,\,0.35\,\,cm\]= 2.2 cm
Area
All the geometrical shapes occupies some space. The occupied space by a geometrical shape is called area of that geometrical shape.
Shaded part in the above figures represent area.
Unit of the area is \[cm_{{}}^{2}\] or\[mr_{{}}^{2}\].
Area of a Triangle
Area of a triangle \[=\,\,\frac{1}{2}\] base \[\times \]height.
Where base is the one side of a triangle and height is length of line segment drawn \[90{}^\circ \]on the base of that triangle.
Find the area of the triangle whose base is 75 cm and height is 80 cm.
Solution:
Area of the triangle \[=\,\,\frac{1}{2}\,\,\times \,\,75\,\,cm\,\,\times \,\,80\,\,cm\,\,=\,\,3000\,\,cm_{{}}^{2}\]
Area of a Rectangle
Area of a rectangle \[=\,\,length\,\,\times \,\,breadth.\]
Area of the rectangle PQRS \[=\,\,PQ\,\,\times \,\,QR.\]
Find the area of the rectangle whose length is 17 cm and breadth is 15 cm.
Solution:
Area of the rectangle \[=\,\,17\,\,cm\,\,\times \,\,15\,\,cm\,\,=\,\,255\,\,cm_{{}}^{2}\]
Area of a Square
Area of a square \[=\,\,side_{{}}^{2}\,=\,\,side\,\,\times \,\,side\]
Area of the square PQRS \[=\,\,PQ\,\,\times \,\,PQ\,\,=\,\,PQ_{{}}^{2}.\]
Find the area of the square whose length of each side is 21 cm.
Solution:
Area of the square \[=\,\,21\,\,cm\,\,\times \,\,21\,\,cm\,\,=\,\,441\,\,cm_{{}}^{2}\]
Area of a Circle
Area of the circle \[=\,\,\pi \,\,r_{{}}^{2}\]
Where \[\pi \,\,=\,\,\frac{22}{7}\,\,=\,\,3.14\]
Find the area of the circle whose radius is 0.28 cm.
Solution:
Area of a circle\[=\,\,\frac{22}{7}\,\,\times \,\,0.28\,\,cm\,\,\times \,\,0.28\,\,cm\,\,=\,\,0.2464\,\,cm_{{}}^{2}\]
Volume
In our daily life the number of things is stored in different kinds of container. Holding capacity of a container is called volume.
Volume of a Cuboid
Volume of a cuboid \[=\,\,length\,\,\times \,\,breadth\,\,\times \,\,height=\,\,lbh.\]
Where, length = AB, breadth = AE and height = BC
Volume of the cuboid ABCDEFG \[=\,\,AB\,\,\times \,\,BC\,\,\times \,\,AE.\]
Find the volume of the cuboid whose length, breadth and height are 15 cm, 13 cm and 14 cm respectively.
Solution:
Volume of the cuboid \[=\,\,15\,\,cm\,\,\times \,\,13\,\,cm\,\,\times \,\,14\,\,cm\,\,=\,\,2730\,\,cm_{{}}^{2}\]
Volume of a Cube
Volume of a cube \[=\,\,side_{{}}^{3}\,\,=\,\,side\,\,\times \,\,side\,\,\times \,\,side\,\]
Find the volume of the cube whose length is 19 cm.
Solution:
Volume of the cube \[=\,\,19\,\,cm\,\,\times \,\,19\,\,cm\,\,\times \,\,19\,\,cm\,\,=\,\,6859\,\,cm_{{}}^{3}\]
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