Question

If a rectangle is cut into two equal triangles, what will be the area of each triangle?

• A. Twice the area of the rectangle.
• B. Half the area of the rectangle.
• C. Thrice the area of the rectangle.
• D. None of the above.

Answer 1

Let $ABCD$ is a rectangle with length $l$ and breadth $b$.

Now, Area of rectangle $=l\times b$ sq.units---(1)

Now, the rectangle is cut into two equal triangles then it is divided into two congruent triangles. $\Delta ABC,\Delta CDA$.

$\Rightarrow$ Area of $\Delta ABC=\frac{1}{2}\times l\times b$ sq.units

$\Rightarrow$ Area of $\Delta ABC=\frac{1}{2}$ $\times$ area of rectangle $ABCD$ [Since, from (1)]

Similar way, area of $\Delta CDA=\frac{1}{2}$ $\times$ area of rectangle $ABCD$

Therefore, area of the triangle is half the area of the rectangle

Hence, the correct option is $B$.