Question: Find the area of the kite.
4 m
5 m
10 m
4 m
[?] m²
Kite diagram: the vertices are left, top, right, and bottom; the diagonals intersect at the center. The vertical diagonal is split into 4 m above the center and 4 m below the center. The horizontal diagonal is split into 5 m to the left of the center and 10 m to the right of the center. position_hint = center
1. **State the problem:** We need to find the area of a kite given the lengths of its diagonals.
2. **Recall the formula for the area of a kite:**
$$\text{Area} = \frac{1}{2} \times d_1 \times d_2$$
where $d_1$ and $d_2$ are the lengths of the diagonals.
3. **Identify the diagonals:**
- The vertical diagonal is split into two parts: $4$ m above and $4$ m below the center, so its total length is:
$$d_1 = 4 + 4 = 8$$
- The horizontal diagonal is split into two parts: $5$ m to the left and $10$ m to the right, so its total length is:
$$d_2 = 5 + 10 = 15$$
4. **Calculate the area:**
$$\text{Area} = \frac{1}{2} \times 8 \times 15$$
5. **Simplify the multiplication:**
$$\text{Area} = \frac{1}{2} \times 120$$
6. **Simplify the fraction:**
$$\text{Area} = \cancel{\frac{1}{2}} \times \cancel{120} = 60$$
7. **Final answer:**
The area of the kite is $60$ square meters.