Question

Chapter mensuration class 8th all formulas .

Answer 1

$area \: \: of \: \: trapeium \: = \frac{1}{2} \times (sum \: \: of \: \: parallel \: \: sides) \times distance \: \: between \: \: them \\ \\ surface \: \: area \: \: of \: \: cuboid \: = 2(lb + bh + lh) \\ \\ \ surface \: \: area \: \: of \: \: cube = 6 \times {(side)}^{2} \\ \\ \ surface \: \: area \: \: of \: \: cylinder = 2\pi \: r(r + h) \\ \\ lateral \: \: surface \: \: area \: \: of \: cuboid \: = 2(l + b) \times h \\ \\ lateral \: \: surface \: \: area \: \: of \: cube \: = 4 \times {(side)}^{2} \\ \\ lateral \: \: surface \: \: area \: \: of \: cylinder \: = 2\pi \: rh \\ \\ volume \: \: of \: \: cuboid \: = l \times b \times h \\ \\ volume \: \: of \: \: cube = {(side)}^{3} \\ \\ volume \: \: of \: \: cylinder = \pi {r}^{2} h$

Answer 2

1. Area of rectangle (A) = length(l) × Breath(b)

A = l \times b



2. Perimeter of a rectangle (P) = 2 × (Length(l) + Breath(b))

P = 2 \times(l + b)



3. Area of a square (A) = Length (l) × Length (l)

A = l \times l



4. Perimeter of a square (P) = 4 × Length (l)

P = 4 \times l



5. Area of a parallelogram(A) = Length(l) × Height(h)

A = l \times h

Parallelogram



6. Perimeter of a parallelogram (P) = 2 × (length(l) + Breadth(b))

P = 2 \times (l + b)



7. Area of a triangle (A) = (Base(b) × Height(b)) / 2

A = \frac{1}{2} \times b \times h

Triangle

And for a triangle with sides measuring “a” , “b” and “c” , Perimeter = a+b+c

and s = semi perimeter = perimeter / 2 = (a+b+c)/2

And also: Area of triangle = A = \sqrt{s(s-a)(s-b)(s-c)}

This formulas is also knows as “Heron’s formula”.



8. Area of triangle(A) = \frac{1}{2} a \times b \times \angle C = \frac{1}{2} b \times c \times \angle A = \frac{1}{2} a \times c \times \angle B

Where A, B and C are the vertex and angle A , B , C are respective angles of triangles and a , b , c are the respective opposite sides of the angles as shown in figure below:

area of triangle - mensuration
area of triangle - mensuration



9. Area of isosceles triangle = \frac{b}{4}\sqrt{4a^2 - b^2}

Where a = length of two equal side , b= length of base of isosceles triangle.



10. Area of trapezium (A) = \frac{1}{2} (a+b) \times h