To find the area of one triangular shelf, we can use the formula for the area of a triangle given two sides and the included angle:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
where:
- \( a \) and \( b \) are the lengths of the two sides,
- \( C \) is the angle between those sides.
Given:
- \( a = 22 \) inches
- \( b = 35 \) inches
- Angle \( C = 87^\circ \)
Let's calculate the area of one shelf:
-
Calculate \(\sin(87^\circ)\): \[ \sin(87^\circ) \approx 0.998 \]
-
Plug the values into the area formula: \[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times 0.998 \]
-
Calculate: \[ \text{Area} = \frac{1}{2} \times 770 \times 0.998 \] \[ \text{Area} \approx \frac{770 \times 0.998}{2} \approx \frac{767.46}{2} \approx 383.73 \text{ square inches} \]
-
Round to the nearest square inch: \[ \text{Area} \approx 384 \text{ square inches} \]
Since Jasmira has three identical shelves, the total area covered by the shelving paper will be:
\[ \text{Total Area} = 3 \times 384 \approx 1152 \text{ square inches} \]
Thus, rounding to the nearest square inch, the total area is:
\[ \text{Total Area} \approx 1152 \text{ square inches} \]
However, we should check the options given closely. The nearest square inch calculated is closest to 1,153 inches².
Therefore, the answer is:
1,153 inches squared.