- If 'l', 'w' and 'h' are the length, width and height of a room and 'A' the total area of the four walls then A = 2h(l+w) sq units.
- If the perimeter of the floor of a room is 'p', its height is 'h' and the total area of the four walls is 'A' then, A = ph sq units.
- If the floor of a room is in the shape of a square whose side is 'l' and 'h' is the height of the room and 'A' denotes the total area of the four walls, then A = 4lh sq units.
- If a rectangular path of uniform width surrounds a rectangle then the length and the breadth of the outer rectangle are obtained by adding twice the width of the path to the length and the width of the inner rectangle.
- If 'l', 'w', 'h' are the length, width and height of a cuboid, then its
- Lateral surface area = 2h(l+w) sq units.
- Total surface area = 2(lw + wh + hl) sq units.
- A cuboid in which the length, the width and the height are equal is called a cube.
- If 'l' is the edge of a cube then its,
- Lateral surface area = 4l2 sq units.
- Total surface area is 6l2sq units.
- The area of a triangle = 1/2 * base * height sq units.
- The area of a right triangle = 1/2(Product of the sides containing the right angle) sq units.
- If 'b' denotes any side of a parallelogram and 'h' denotes the height relative to this side, then area of the parallelogram is given by, A = bh sq units.
- If 'd1' and 'd2' are the diagonals of a rhombus and its area be 'A' then,
A = 1/2 * d1d2 sq units.
- If 'a' and 'b' are the length of the parallel sides of a trapezium, 'h' the distance between them and 'A' its area then,
A = 1/2 * (a+b)*h sq units.
- If the diameter of a circle is 'd' and its radius is 'r' then d = 2r.
- p = The circumference of a circle / The diameter of the circle.
- Circumference of a circle = p * diameter.
- Circumference of a circle = 2p * radius of the circle.
- The area A of a circle radius r is given by, A = p
r2 sq units.
- If the radii of the outer and inner circles having the same center are 'R' and 'r' and then area of the ring so formed is A.
A = pR2 - pr2 sq units.
- If the radius of a circle is 'r' and an arc AB on the circle subtends angle 'X°' at the center 'O' then.
- The length 'l' of the arc AB is given by l = X/360 * 2pr sq units.
- The area A of the sector OAB is given by, A = X/360 * pr2 sq units.
- Also A = 1/2 *l *r sq units.
- If 'l', 'w' and 'h' denote the length, width and height of a cuboid and 'V' its volume then,
V = l*b*h sq units.
- The volume 'V' of a cube whose edge (or side) is equal to 'S' is given by,
V = S3 cubic units.
- Area of quadrilateral A = 1/2 * d (h1 + h2), where 'd' is the diagonal 'h1' and 'h2' are the perpendiculars drawn to the diagonal.
- Rising in the level = Volume of the soil spread / Area of the remaining plot.
- If the outer dimensions of a metal box of thickness 't' are 'l', 'b' and 'h', then the inner dimensions are l-2t, b-2t, h-2t.
- A cuboid has 6 faces, 12 edges and 8 vertices then,
- Faces + Vertices = Edge + 2;
ie 6 + 8 = 12 + 2 = 14.
Directions: Review all the above formulas and write on a sheet of paper.