The area of the plate covered by the napkin is 56.25 square centimeters and this can be determined by using the formula of perimeter and area of the triangle.
Given :
- A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate.
- The napkin has a perimeter of 38 centimeters.
The following steps can be used in order to determine the area of the plate covered by the napkin:
Step 1 - The formula of the perimeter of a triangle is given below:
P = a + b + c --- (1)
where a, b, and c are the length of the sides of the triangle.
Step 2 - According to the given data, the triangle is isosceles. Therefore, the two sides are similar and the length of the base is 8 cm.
Step 3 - Now, substitute the values of the known terms in the above formula.
38 = 2L + 8
38 - 8 = 2L
L = 15 cm
Step 4 - The area of the plate covered by the napkin is given below:
[tex]\rm A = \dfrac{1}{2}\times 15 \times 15 \times sin30[/tex]
Step 5 - Simplify the above expression.
[tex]\rm A = 56.25 \;cm^2[/tex]
For more information, refer to the link given below:
https://brainly.com/question/15442893
