Question

A triangle and a parrallelogram have same base and height what will be the ratio of area of triangle and area of parallelogram?

Answer 1

Answer:

1:2

Step-by-step explanation:

Consider a parallelogram ABCD (see fig.). Its diagonal BD divides its into two triangles ADB and CDB.

Draw DX and CY perpendiculars on AB.

DX = CY because AB and CD are parallel lines because ABCD is a parallelogram.

Let DX = CY = h.

Then, Area Parallelogram = Base*Height = AB*CY = AB*h

Now, Area of triangle = (1/2) Base * Height = (1/2)AB*DX = (1/2)AB*h

Ratio of area of parallelogram to area of triangle = AB*h / (1/2)AB*h = AB*h * 2/AB*h = 1/2 = 1:2

This also means that the area of triangle is half of the area of the parallelogram. Thanks!