Question: The shaded triangle has an area of 42 cm^2.
Find the area of the entire rectangle.
Be sure to include the correct unit in your answer.
Shaded triangle inside a tall rectangle is split by a diagonal from the top-left corner to the bottom-right corner; the triangle occupies the left half of the rectangle.
1. **State the problem:** We are given a rectangle divided by its diagonal into two triangles. The shaded triangle has an area of $42\ \text{cm}^2$. We need to find the area of the entire rectangle.
2. **Recall the formula for the area of a triangle:**
$$\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$$
3. **Important rule:** The diagonal of a rectangle divides it into two congruent triangles of equal area.
4. Since the shaded triangle is exactly half of the rectangle, the area of the rectangle is twice the area of the shaded triangle.
5. Calculate the area of the rectangle:
$$\text{Area of rectangle} = 2 \times 42 = 84\ \text{cm}^2$$
6. **Final answer:** The area of the entire rectangle is $84\ \text{cm}^2$.