Home
Class 11
PHYSICS
Using the method of integration show tha...

Using the method of integration show that the area of triangle of base b and altitude h is `1/2bh`.

Text Solution

Verified by Experts

Let ABC be the triangle with base `BC=b` and altitude `AM=h`.
Let us consider a thin strip DE on the triangle of thickness `dx`, at a distance x from the vertex A, parallel to the base BC.

If y be the length of the strip DE, then form similar triangles
ABC and ABC, we have `y/x=b/h`.
`impliesy=(bx)/(h)`
Therefore, the area of the rectangular strip DE is given by
`dA=ydx=(bxdx)/(h)`
The complete area of the triangle can be obtained by summing up (integration) the area of individual strips such as DE.
`A=sumdA=underset0oversethint(bxdx)/(h)=b/h[x/2]^h=(b)/(2h)(h^2-0)=1/2bh`
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    CENGAGE PHYSICS|Exercise Exercise 2.1|2 Videos

  • BASIC MATHEMATICS

    CENGAGE PHYSICS|Exercise Exercise 2.2|3 Videos

  • BASIC MATHEMATICS

    CENGAGE PHYSICS|Exercise Exercise 2.6|20 Videos

  • ARCHIVES 2 VOLUME 6

    CENGAGE PHYSICS|Exercise Integer|4 Videos

  • CALORIMETRY

    CENGAGE PHYSICS|Exercise Solved Example|13 Videos

Similar Questions

Explore conceptually related problems

Using the method of integration show that area of circle is pi R^(2) .

Using the method of integration, show that the volume of a right circular cone of base radius r and height h is V=1/3pir^2h .

Find the area of a triangle whose base and altitudes are 8cm and 5cm.

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2,0),B(4,5) and C(6,3) .

Using the method of integration,find the area of the triangle ABC, coordinates of whose vertices are A(1,2),B(2,0) and C(4,3)

Using the method of integration find the area bounded by the curve |x|+|y|=1.

Using the method of integration, find the area of the triangular region whose vertices are (2,-2), (4,3) and (1,2).

Area of triangle by using integration

Find the altitude of a triangle whose base is 20cm and area is 150cm^(2).

Compare the area of a rectangle with base b and height h with the area of a rectangle with base 2b and height 2h.