Question

1. a triangle has a base of (3x + 1) cm and height of 4 cm. write an expression for the area.

(remember: area = 1/2 × base × height)

Explanation:

Step1: Substitute the values into the formula

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Given \(base=(3x + 1)\) cm and \(height = 4\) cm. Substitute these values into the formula: \(A=\frac{1}{2}\times(3x + 1)\times4\).

Step2: Simplify the expression

First, simplify \(\frac{1}{2}\times4\) which is \(2\). Then, use the distributive property \(a(b + c)=ab+ac\) where \(a = 2\), \(b=3x\), and \(c = 1\). So, \(A=2\times(3x + 1)=2\times3x+2\times1\).

Step3: Calculate the final result

\(2\times3x=6x\) and \(2\times1 = 2\). So the area \(A=(6x + 2)\) \(cm^{2}\).

Answer:

\((6x + 2)\) \(cm^{2}\)