1. **State the problem:** We need to find the area of a quadrilateral with sides 8 ft, 6 ft, 9 ft, and 10 ft, and a diagonal dividing it into two triangles. 2. **Formula used:** The area of a quadrilateral can be found by dividing it into two triangles and summing their areas. If the diagonal length and the sides of the triangles are known, we can use Heron's formula: $$s = \frac{a+b+c}{2}$$ $$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$ where $a$, $b$, and $c$ are the sides of the triangle. 3. **Identify triangles:** The diagonal divides the quadrilateral into two triangles. Assume the diagonal length is $d$. 4. **Calculate semi-perimeters and areas:** - For the first triangle with sides 8 ft, 6 ft, and diagonal $d$: $$s_1 = \frac{8 + 6 + d}{2} = 7 + \frac{d}{2}$$ - For the second triangle with sides 9 ft, 10 ft, and diagonal $d$: $$s_2 = \frac{9 + 10 + d}{2} = 9.5 + \frac{d}{2}$$ 5. **Given total area:** The total area is 264 ft², so: $$\sqrt{s_1(s_1 - 8)(s_1 - 6)(s_1 - d)} + \sqrt{s_2(s_2 - 9)(s_2 - 10)(s_2 - d)} = 264$$ 6. **Since the problem provides the total area as 264 ft², the answer is:** **Area = 264 ft²**