Mid-point area
M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?
Age
11 to 14
Challenge level
Problem
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$M$ is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle $PMR$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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$M$ is the midpoint of the side of the rectangle, so $RM$ has length $2$ units.
Letting RM be the base of the triangle:
\begin{eqnarray} \text{Area of Triangle } PMR & = & \frac{1}{2} \times \text{base} \times \text{height} \\ & = & \frac{1}{2} \times 2 \; \text{units} \times 3 \; \text{units} \\ &=& 3 \; \text{square units}\end{eqnarray}