Respuesta :
The area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].
What is an area of a triangle?
- The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.
- Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.
- As a result, in order to calculate the area of a triangular polygon, we must first determine its base (b) and height (h).
To find the area of the plate covered by the napkin:
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]A=\frac{1}{2} * 15 * 15 *Sin30[/tex]
Step 5 - Simplify the above expression.
[tex]A=56.25cm^{2}[/tex]
Rounding off to the nearest whole number, which is [tex]56cm^{2}[/tex].
Therefore, the area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].
Know more about the area of the triangle here:
https://brainly.com/question/17335144
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The question you are looking for is here:
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. To the nearest square centimeter, how many square centimeters of the plate is covered by the napkin?
(A) 16 square centimeters
(B) 30 square centimeters
(C) 56 square centimeters
(D) 60 square centimeters
