Question

The base of the triangle decreases by 30% and the height increases by 20%.

What is the overall percentage change to the area of the triangle?
State clearly if this is an increase or a decrease.
The base is 18cm
The height is 5cm

Answer 1

Area decreases by 16%

Explanation:

Use formula for the area of the triangle

`A=(1)/(2)\cdot \text{Base}\cdot \text{Height}`

Initial triangle:

The base is 18 cm

The height is 5 cm

The area is

`A_(initial)=(1)/(2)\cdot 18\cdot 5=45\ cm^2`

New triangle:

The base is
`(1-0.3)\cdot 18=0.7\cdot 18=12.6\ cm`

The height is
`(1+0.2)\cdot 5=1.2\cdot 5=6\ cm`

The area is

`A_(new)=(1)/(2)\cdot 12.6\cdot 6=37.8\ cm^2`

Area decreases by

`100\%-(37.8)/(45)\cdot 100\%=100\%-84\%=16\%`