7. Jason used the formula \( A=h\left(\frac{b_{1}+b_{2}}{2}\right) \) to find the area of his yard, which he has drawn on a coordinate plane. Will this give an accurate result? If not, what method would give the correct area?

The formula \( A = h\left(\frac{b_{1}+b_{2}}{2}\right) \) is used to calculate the area of a trapezoid, where \( h \) is the height and \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides. If Jason's yard is shaped like a trapezoid, then using this formula will give an accurate result for the area. However, if the shape of his yard is not a trapezoid (for example, if it is irregular, circular, or has a different polygonal shape), then this formula would not yield the correct area. To find the correct area of an irregular shape, Jason could use one of the following methods: 1. **Grid Method**: If the yard is drawn on a coordinate plane, he could count the number of grid squares that fall within the boundary of the yard. This method works well for irregular shapes. 2. **Polygon Area Formula**: If the yard can be divided into simpler shapes (like triangles and rectangles), he could calculate the area of each shape and sum them up. 3. **Coordinate Geometry**: If the vertices of the yard are known, he could use the shoelace formula (or surveyor's formula) to calculate the area based on the coordinates of the vertices. 4. **Approximation Methods**: For more complex shapes, numerical methods or calculus (like integration) could be used to approximate the area. In summary, if Jason's yard is not a trapezoid, he should consider using one of the above methods to accurately calculate the area.