Use 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 of the letter H, we need to decompose it into simple shapes and calculate the area of each shape separately.
Let's break down the letter H into three simple shapes: two rectangles for the vertical sides and one rectangle for the horizontal bridge.
First, let's calculate the area of each vertical side:
Area of a rectangle = length × width
For the vertical sides:
Area = (6.0 cm) × (0.8 cm) = 4.8 square cm
Next, let's calculate the area of the horizontal bridge:
Area = (2.1 cm) × (0.5 cm) = 1.05 square cm
Now, we can add up the areas of all the shapes to find the total area of the letter H:
Total area of H = 2 × (area of vertical side) + area of horizontal bridge
= 2 × 4.8 square cm + 1.05 square cm
= 9.6 square cm + 1.05 square cm
= 10.65 square cm
Therefore, the artist will need 10.65 square centimeters of gold leaf to cover the initial letter H.
To decompose the letter H into simple shapes, we can break it down into two rectangles and one square.
The first rectangle has a base of 0.8 and a height of 6.0, giving an area of 4.8 square centimeters.
The second rectangle has the same dimensions and area as the first one.
The square in the middle has a side length of 2.1, giving an area of 4.41 square centimeters.
Adding up the areas of all three shapes, the artist will need a total of 14.01 square centimeters of gold leaf.