An artist wants to cover in gold leaf a card with the initial letter shown. Decompose the letter i think the letter’s C. Decompose the letter into simple shapes to find the area. How many square centimeters of gold leaf will the artist need? Do not round your answer.
(1 point)
To decompose the letter "C" into simple shapes, we can break it down into three shapes: two semicircles and a rectangle.
1. One semicircle on the top
2. One semicircle on the bottom
3. One rectangle on the right side
To find the area, we need to calculate the area of each shape and then add them together.
1. Area of semicircle = (1/2) * π * r^2
Assuming the radius, r, is the height of the "C", we'll denote it as h.
Area of top semicircle = (1/2) * π * (h/2)^2 = (1/8) * π * h^2
2. Area of bottom semicircle = (1/8) * π * h^2
3. Area of rectangle = height * width
Assuming the height is h and the width is a quarter of the height, we'll denote it as w.
Area of rectangle = h * (h/4) = (1/4) * h^2
Total area = (1/8) * π * h^2 + (1/8) * π * h^2 + (1/4) * h^2 = (1/4) * π * h^2 + (1/4) * h^2 = (1/4) * (π + 1) * h^2
Now, we need to calculate the area of the gold leaf. Let's assume the height of the "C" is 10 cm.
Area of gold leaf = (1/4) * (π + 1) * (10)^2 = (1/4) * (π + 1) * 100 = (25/4) * (π + 1) ≈ 123.504 cm^2
Therefore, the artist will need approximately 123.504 square centimeters of gold leaf to cover the initial letter "C".