Question

cheyenne has a new corner shelving unit that is triangular. the unit has three identical oblique triangle shelves. cheyenne wants to put some shelving paper down, but isnt sure how much to buy. if one side of each triangle is 22 inches, with an adjoining side is 35 inches, and the angle formed between them is 87 degrees. how much paper (to the nearest square inch) does she need to cover all 3 shelves? (1 point)○ 1,647 inches²○ 2,038 inches²○ 1,153 inches²○ 660 inches²

Explanation:

Step1: Area of one oblique triangle

Use formula for area with two sides & included angle:
$$\text{Area}_1 = \frac{1}{2}ab\sin(C)$$
Substitute $a=22$, $b=35$, $C=87^\circ$:
$$\text{Area}_1 = \frac{1}{2} \times 22 \times 35 \times \sin(87^\circ)$$
Calculate $\sin(87^\circ) \approx 0.9986$:
$$\text{Area}_1 \approx \frac{1}{2} \times 22 \times 35 \times 0.9986 \approx 384.451$$

Step2: Total area for 3 shelves

Multiply single shelf area by 3:
$$\text{Total Area} = 3 \times \text{Area}_1$$
$$\text{Total Area} \approx 3 \times 384.451 \approx 1153.353$$

Step3: Round to nearest square inch

Round the total area:
$$\text{Total Area} \approx 1153$$

Answer:

1,153 inches²