Question

a triangle has a base of 4 units and a height of 3 units. mark draws the triangle again but doubles the height. how does the area of the triangle change? the area increases by 12 square units. the area increases by 3 square units. the area does not change. the area increases by 6 square units.

Explanation:

Step1: Calculate the original area

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Given \(b = 4\) and \(h=3\), then \(A_1=\frac{1}{2}\times4\times3=6\)

Step2: Calculate the new area

The height is doubled, so \(h_2 = 2\times3=6\), \(b = 4\). Then \(A_2=\frac{1}{2}\times4\times6 = 12\)

Step3: Find the change in area

\(\Delta A=A_2 - A_1\), so \(\Delta A=12 - 6=6\)

Answer:

The area increases by 6 square units.