To find the area of the top of the table, we need to calculate the areas of the rectangles and triangles separately and then sum them.
Rectangles
We know there is one rectangle on the table with the following dimensions:
- Length: 100 inches
- Width: 30 inches (since everything else is 30 inches)
The area of the rectangle is calculated using the formula: \[ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 100 , \text{inches} \times 30 , \text{inches} = 3000 , \text{square inches} \]
Triangles
The triangles are placed at the ends of the table, and each triangle has the following dimensions:
- Base (width): 30 inches
- Height: 30 inches
The area of one triangle is calculated using the formula: \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 30 , \text{inches} \times 30 , \text{inches} = \frac{1}{2} \times 900 = 450 , \text{square inches} \]
Since there are two triangles at the ends of the table, the total area contributed by the triangles is: \[ \text{Total Area}{\text{triangles}} = 2 \times \text{Area}{\text{triangle}} = 2 \times 450 , \text{square inches} = 900 , \text{square inches} \]
Total Area of the Table Top
Now, we can sum the areas of the rectangle and the triangles to find the total area of the table top: \[ \text{Total Area}{\text{table}} = \text{Area}{\text{rectangle}} + \text{Total Area}_{\text{triangles}} = 3000 , \text{square inches} + 900 , \text{square inches} = 3900 , \text{square inches} \]
Thus, the area of the top of the table is: \[ \boxed{3900} , \text{square inches} \]