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

Answer:

Area decreases by 16%

Step-by-step explanation:

Use formula for the area of the triangle

$A=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}$

Initial triangle:

The base is 18 cm

The height is 5 cm

The area is

$A_{initial}=\dfrac{1}{2}\cdot 18\cdot 5=45\ cm^2$

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

$A_{new}=\dfrac{1}{2}\cdot 12.6\cdot 6=37.8\ cm^2$

Area decreases by

$100\%-\dfrac{37.8}{45}\cdot 100\%=100\%-84\%=16\%$