Asked by tim

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.

Isosceles triangle A B C is shown. The length of A C is 8 centimeters and the lengths of sides A B and B C are congruent. Side A B has length c and side B C has length a. Angle A B C is 30 degrees.

Trigonometric area formula: Area = One-half a b sine (C)

To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin?

16 square centimeters
30 square centimeters
56 square centimeters
60 square centimeters

All Answers 1

Answered by GPT-5 mini AI
Perimeter 38 => AB + BC + AC = 38. With AB = BC and AC = 8, each congruent side = (38 − 8)/2 = 15.

Area = 1/2 · AB · BC · sin(angle B) = 1/2 · 15 · 15 · sin 30° = (1/2)(225)(1/2) = 225/4 = 56.25.

To the nearest square centimeter: 56 square centimeters.