To determine the area of one triangular shelf and then find the total area for all three shelves, we can use the formula for the area of a triangle given two sides and the included angle:
\[ \text{Area} = \frac{1}{2}ab \sin(C) \]
Where:
- \(a\) and \(b\) are the lengths of the sides,
- \(C\) is the included angle.
In this case:
- \(a = 22\) inches,
- \(b = 35\) inches,
- \(C = 87^\circ\).
First, we calculate the sine of 87 degrees:
\[ \sin(87^\circ) \approx 0.998 \]
Now, substituting the values into the area formula:
\[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ) \] \[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times 0.998 \] \[ \text{Area} = 0.5 \times 22 \times 35 \times 0.998 \]
Calculating \( 0.5 \times 22 \times 35 \):
\[ 0.5 \times 22 = 11 \] \[ 11 \times 35 = 385 \]
Now multiply by \(0.998\):
\[ \text{Area} \approx 385 \times 0.998 \approx 384.23 \]
So, the area of one triangular shelf is approximately \(384.23\) square inches. For all three shelves, we multiply this area by 3:
\[ \text{Total Area} = 3 \times 384.23 \approx 1152.69 \]
Rounding this to the nearest whole number gives:
\[ \text{Total Area} \approx 1153 \text{ square inches} \]
Therefore, the amount of shelving paper Jasmira needs to buy is approximately:
\[ \boxed{1153} \text{ square inches} \]
The closest answer from the options provided is A. 1,153 inches².