A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. the napkin has a perimeter of 48 centimeters. trigonometric area formula: Area = 1/2abSin(c). To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin? show your work for full credit.

The area of plate which is covered by the napkin is equal to the area of folded napkin.

Before finding the area of folded napkin, we should find the dimension of the napkin.
Find the length of the leg side, the two leg has similar length.
perimeter = 38
l + l + 8 = 38
2l + 8 = 38
2l = 30
l = 15
Each leg is 15 cm long.

Find the area of folded napkin
area = 1/2 × s × s × sin of angle between the sides
area = 1/2 × 15 × 15 × sin 30°
area = 1/2 × 15 × 15 × 1/2
area = 225/4
area = 56.25
to the nearest whole number >> 56 cm²
The answer is third option