Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?
To find the total area of the piece of jewelry, we need to calculate the area of each individual shape and then sum them up.
The piece of jewelry consists of a triangle with base 4 cm and height 3 cm, a rectangle with length 6 cm and width 3 cm, and a semicircle with radius 3 cm.
1. Area of the triangle = 1/2 * base * height = 1/2 * 4 * 3 = 6 cm²
2. Area of the rectangle = length * width = 6 * 3 = 18 cm²
3. Area of the semicircle = 1/2 * π * radius² = 1/2 * π * 3² = 4.5π cm²
Now, summing up the areas of the three shapes:
Total area = 6 cm² + 18 cm² + 4.5π cm² ≈ 6 cm² + 18 cm² + 14.13 cm² ≈ 38.13 cm²
Therefore, the total area of the piece of jewelry is approximately 38.13 square centimeters.