se the image to answer the question.
An illustration shows the outline of an uppercase letter H. The vertical sides are labeled as 6.0, and the base of each leg is 0.8. The length of the horizontal bridge in the middle is 2.1, and the width is 0.5, denoted by a dashed line on the right side.
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?
(1 point)
The artist will need
square centimeters of gold leaf.
To find the area, we need to decompose the letter H into simple shapes. We can see that the letter is made up of two rectangles (the vertical sides) and one rectangle with two semi-circles attached (the horizontal bridge).
The area of the vertical sides is:
6.0 x 0.8 = 4.8 square centimeters (each side)
The area of the horizontal bridge can be broken down into a rectangle and two semi-circles. The rectangle has dimensions 2.1 (length) x 0.5 (width) = 1.05 square centimeters. The two semi-circles have radii of 0.5 (half the width of the rectangle) and their combined area is:
0.5 x 0.5 x π = 0.25π square centimeters
So the total area of the letter H is:
4.8 + 4.8 + 1.05 + 0.25π = 11.45 + 0.785 square centimeters
= 12.235 square centimeters (rounded to three decimal places)
Therefore, the artist will need approximately 12.235 square centimeters of gold leaf.