Question

the top of the table is made up of triangles and rectangles. the table and its deminsions in inches
what is the area of the top of the table in square inches?
two right triangles 30in x 30in
2 rectangles 30x100
1 rectangle 30x 30

Answer 1

To find the total area of the top of the table, you need to calculate the area of each component (triangles and rectangles) and then sum them up.

### Areas of the Components

1. **Right Triangles**:
For one right triangle, the area is given by the formula:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Each triangle has a base of 30 inches and a height of 30 inches.
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 30 \times 30 = 450 \text{ square inches}
\]
Since there are 2 triangles:
\[
\text{Total Area}_{\text{triangles}} = 2 \times 450 = 900 \text{ square inches}
\]

2. **Rectangles**:
- For the first rectangle (30 x 100):
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 30 \times 100 = 3000 \text{ square inches}
\]
- For the second rectangle (30 x 100, same dimensions as the first):
\[
\text{Area}_{\text{rectangle}} = 30 \times 100 = 3000 \text{ square inches}
\]
- For the third rectangle (30 x 30):
\[
\text{Area}_{\text{rectangle}} = 30 \times 30 = 900 \text{ square inches}
\]

### Total Areas of Rectangles:
\[
\text{Total Area}_{\text{rectangles}} = 3000 + 3000 + 900 = 6900 \text{ square inches}
\]

### Total Area of the Table Top:
Now, adding the areas of the triangles and rectangles together:
\[
\text{Total Area}_{\text{table}} = \text{Total Area}_{\text{triangles}} + \text{Total Area}_{\text{rectangles}}
\]
\[
\text{Total Area}_{\text{table}} = 900 + 6900 = 7800 \text{ square inches}
\]

Therefore, the area of the top of the table is **7800 square inches**.