Question

In triangle abc, bc=4cm, ad=3cm. The triangle abc moves upward at the speed of 4cm per seconds. What is the area swept by the triangle in three seconds?

Answer 1

Explanation:

Area Of Triangle And Rectangle

Given a triangle of base b and height h (perpendicular to b), the area can be computed by

`\displaystyle A=(bh)/(2)`

A rectangle of the same dimensions has an area of

`A=bh`

We have a triangle of base 3 cm and a height of 4 cm. Its area is

`\displaystyle A=((3)(4))/(2)=6\ cm^2`

That triangle moves upward at 4 cm per second for 3 seconds. It means that the triangle 'sweeps' upwards three times its height forming a rectangle of base 3 cm and height 12 cm. The area of the swept area is

`A=(3)(12)=36\ cm^2`

The triangle stays in the top of this rectangle, so its area is part of the total swept area:

Total swept area = 6 + 36 =
`42\ cm^2`