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 3 square units.
the area increases by 6 square units.
the area increases by 12 square units.
the area does not change.

Explanation:

Step1: Calculate the original area

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).
Given \(base = 4\) units and \(height=3\) units.
\(A_1=\frac{1}{2}\times4\times3=6\) square units.

Step2: Calculate the new area

The height is doubled, so new height \(h = 2\times3 = 6\) units.
Using the area formula \(A=\frac{1}{2}\times base\times height\) with \(base = 4\) units and \(height = 6\) units.
\(A_2=\frac{1}{2}\times4\times6 = 12\) square units.

Step3: Find the difference in areas

\(\Delta A=A_2 - A_1\).
\(\Delta A=12 - 6=6\) square units.

Answer:

The area increases by 6 square units.