1. **State the problem:** Find the area of the given shape with sides 9 ft, 6 ft, 17 ft, and 4 ft. 2. **Analyze the shape:** The shape appears to be a quadrilateral. To find its area, we can divide it into simpler shapes such as triangles or rectangles. 3. **Use the formula:** If the shape is irregular, one approach is to divide it into two triangles and use Heron's formula for each. 4. **Calculate the area of each triangle:** - For a triangle with sides $a$, $b$, and $c$, the semi-perimeter is $$s = \frac{a+b+c}{2}$$ - The area is $$\sqrt{s(s-a)(s-b)(s-c)}$$ 5. **Apply to the first triangle:** Assume the first triangle has sides 9 ft, 6 ft, and 17 ft. - Calculate semi-perimeter: $$s = \frac{9 + 6 + 17}{2} = \frac{32}{2} = 16$$ - Calculate area: $$\sqrt{16(16-9)(16-6)(16-17)} = \sqrt{16 \times 7 \times 10 \times (-1)}$$ - Since one term is negative, this triangle is not valid with these sides. 6. **Reconsider the shape:** The sides 9 ft, 6 ft, 17 ft, and 4 ft likely form a trapezoid or composite shape. Let's assume it's a trapezoid with bases 17 ft and 9 ft, and height 6 ft. 7. **Use trapezoid area formula:** $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times \text{height}$$ 8. **Calculate area:** $$\frac{(17 + 9)}{2} \times 6 = \frac{26}{2} \times 6 = 13 \times 6 = 78$$ 9. **Final answer:** The area of the shape is **78 square feet**.