An artist wants to cover in gold leaf a card with initial letter decomposed 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. The artist will need___ Square centimeters of gold leaf.

Answer 1

To calculate the area of the gold leaf needed, we first need to find the areas of the simple shapes composing the initial letter.

Let's say the initial letter is "S" and it is decomposed into a rectangle and two circles. The dimensions of the rectangle are 4 cm x 2 cm and the radius of the circles are 1 cm each.

The area of the rectangle is:
Area_rectangle = length x width = 4 cm x 2 cm = 8 square cm

The area of one circle is:
Area_circle = πr^2 = π x (1 cm)^2 = π square cm

Since there are two circles, the total area of the circles is:
Total_area_circles = 2 x Area_circle = 2π square cm

Therefore, the total area of gold leaf needed is:
Total_area_gold_leaf = Area_rectangle + Total_area_circles = 8 square cm + 2π square cm

The artist will need 8 square centimeters of gold leaf.