To determine the area of one of the triangular shelves, 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 included angle.
For Jasmira's shelves:
- \( a = 22 \) inches,
- \( b = 35 \) inches,
- \( C = 87^\circ \).
First, we need to find the sine of the angle:
\[ \sin(87^\circ) \approx 0.998 \]
Now we calculate the area of one triangle:
\[ \text{Area} = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ) \] \[ \text{Area} \approx \frac{1}{2} \times 22 \times 35 \times 0.998 \] \[ \text{Area} \approx \frac{1}{2} \times 770 \times 0.998 \] \[ \text{Area} \approx 385 \times 0.998 \approx 384.93 \]
Now the area of one triangular shelf is approximately \( 385 \) square inches (when rounded).
Since there are 3 shelves, we multiply the area of one shelf by 3:
\[ \text{Total Area} = 3 \times 384.93 \approx 1154.79 \]
Rounding this to the nearest square inch gives approximately \( 1155 \) square inches for the total area of the three shelves.
So Jasmira would need to buy about 1,155 inches² of shelving paper.
However, based on the provided answers, it looks like the total area would be considered as 1,153 inches². Therefore, the correct response to select would be:
1,153 inches² (to the nearest square inch).
1 answer