An artist wants to cover in gold leaf a card with the initial letter shown. 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. 6, 0.8, 2.1, 0.5, 0.8

1 answer

To decompose the letter into simple shapes, we can see that the letter "D" can be broken down into a rectangle and a semicircle.

First, let's calculate the area of the rectangle:
Height of rectangle = 6 cm
Width of rectangle = 2.1 cm
Area of rectangle = 6 cm * 2.1 cm = 12.6 square cm

Next, let's calculate the area of the semicircle:
Radius of semicircle = 0.8 cm
Area of semicircle = 0.5 * π * (0.8 cm)^2 = 1.00530964915 square cm

Total area of the letter "D":
Total area = Area of rectangle + Area of semicircle
Total area = 12.6 square cm + 1.00530964915 square cm = 13.60530964915 square cm

Therefore, the artist will need 13.60530964915 square centimeters of gold leaf to cover the card with the initial letter "D".