Mensuration~~Quadrilateral

Quadrilateral
1. Square
2. Rectangle
3. Rhombus
4. Parallelogram
5. Trapezium

1. Square ( having equal sides n 90° angle btn any two side...)

Area = a² = d²/2
Perimeter = 4a
Diagonal = √2 a

2. Rhombus ( having equal sides but angle btn any two sides is not equal to 90°

Area = ½*d1*d2 (**d1 and d2 are diagonal)
Area = base*height
Perimeter = 4a

a²=(d1/2)² + (d2/2)²

3. Rectangle (opposite sides are equal , parallel and angle btn any two sides is of 90°)

Area = length*breadth
D² = L² + B²
Perimeter = 2(L+B)

When a road is built parallel to sides of the field but not adjacent to them,

total area of road=lx+bx-x² =x(l+b-x)   (where x² is common area)

when road is built adjacent to sides

in case of inner side
area of road=2x(l+b-2x)


in case of outer side
area of road = 2x(l+b+2x)

4. Parallelogram ( opposite sides are equal,parallel but angle btn any two sides is not 90°)

Area = ab sinφ  (φ is the angle btn a and b)
Area = base*height
Perimeter = 2(a+b)  (**where a and b are adjacent sides )
(d1²+d2²)/2 = a² + b²
d1=√(a² + b² +2ab cosφ)
(d1 is the diagonal starting from the common/meeting point of a and b and cosφ is the angle btn a and b

5. Trapezium ( all sides having different lengths and none of the angle is of 90°)

Area = ½* height * (a+b)    (**where a and b are parallel sides )