Algebraic Techniques, SM-Bank 137

The triangle below has a base of \((2+6\large m)\) and a perpendicular height of \(\large m\).

Write an algebraic expression and expand it to represent the area of the triangle. (2 marks)

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\(x^2+xy\)

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\(\text{Area of Triangle}\)	\(=\dfrac{1}{2}\times \text{base} \times \text{height}\)
	\(=\dfrac{1}{2}\times \Big(2+6m\Big)\times m\)
	\(=\dfrac{m}{2}\Big(2+6m\Big)\)
	\(=\dfrac{m}{2}\times 2 +\dfrac{m}{2}\times 6m\)
	\(=m+3m^2\)