Question

Look at the drawing of a triangle within a rectangle. The triangle and the rectangle have the same base, and heighth If the area of the triangle is 48 square units, what is the total area of sections 1 and 2?

Answer 1

The area of a triangle is given by the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

According to your information, the area of the triangle is 48 square units. We can set up the equation:

\[
48 = \frac{1}{2} \times \text{base} \times \text{height}
\]

To find the area of the rectangle, we note that the area of the rectangle is given by the formula:

\[
\text{Area of rectangle} = \text{base} \times \text{height}
\]

Since the rectangle has the same base and height as the triangle, we can express the area of the rectangle as:

\[
\text{Area of rectangle} = \text{base} \times \text{height} = 2 \times \text{Area of triangle}
\]

Since the area of the triangle is 48 square units, we can determine the area of the rectangle as follows:

\[
\text{Area of rectangle} = 2 \times 48 = 96 \text{ square units}
\]

Now, to find the total area of sections 1 and 2 (the area of the rectangle minus the area of the triangle), we compute:

\[
\text{Area of sections 1 and 2} = \text{Area of rectangle} - \text{Area of triangle} = 96 - 48 = 48 \text{ square units}
\]

Thus, the total area of sections 1 and 2 is:

\[
\boxed{48} \text{ square units}
\]