Question

A triangular garden has an area of 9 square yards. Which figure could represent the garden?
A triangle has a base of 9 yards and height of 9 yards.
A triangle has a base of 6 yards and a height of 6 yards.

A triangle has a base of 3 yards and a height of 6 yards.

A triangle has a base of 3 yards and a height of 3 yards.

Answer 1

To determine which triangle could represent a garden with an area of 9 square yards, we can use the formula for the area of a triangle:

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

Now, let's calculate the area for each option:

1. **Triangle with a base of 9 yards and a height of 9 yards:**
\[
\text{Area} = \frac{1}{2} \times 9 \times 9 = \frac{1}{2} \times 81 = 40.5 \text{ square yards}
\]

2. **Triangle with a base of 6 yards and a height of 6 yards:**
\[
\text{Area} = \frac{1}{2} \times 6 \times 6 = \frac{1}{2} \times 36 = 18 \text{ square yards}
\]

3. **Triangle with a base of 3 yards and a height of 6 yards:**
\[
\text{Area} = \frac{1}{2} \times 3 \times 6 = \frac{1}{2} \times 18 = 9 \text{ square yards}
\]

4. **Triangle with a base of 3 yards and a height of 3 yards:**
\[
\text{Area} = \frac{1}{2} \times 3 \times 3 = \frac{1}{2} \times 9 = 4.5 \text{ square yards}
\]

From these calculations, the only triangle that has an area of 9 square yards is the third option:

**A triangle with a base of 3 yards and a height of 6 yards.**