A composite shape is drawn using a rectangle and 2 triangles. A horizontally aligned rectangle is 9 centimeters long and 3 centimeters wide. A right triangle facing upward adjoins the rectangle on the left side marked 3 centimeters. A right triangle facing downward adjoins the rectangle on the right side. The base leg of both triangles measures 2 centimeters.

Question

Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?

(1 point)
Responses

39 square centimeters
39 square centimeters

30 square centimeters
30 square centimeters

33 square centimeters
33 square centimeters

27 square centimeters

Answer 1

To find the total area of the piece of jewelry composed of a rectangle and two triangles, we'll calculate the area of each shape separately and then sum them up.

1. Area of the rectangle:

   • Length = 9 cm
   • Width = 3 cm
   • Area = Length × Width = 9 cm × 3 cm = 27 square centimeters

2. Area of the triangles: Each triangle is a right triangle with a base (the leg) measuring 2 cm and a height of 3 cm.

   • Area of one triangle = 0.5 × base × height = 0.5 × 2 cm × 3 cm = 3 square centimeters
   • There are two triangles, so the total area of the triangles = 2 × 3 square centimeters = 6 square centimeters

3. Total area of the piece of jewelry:

   • Total area = Area of the rectangle + Area of the triangles
   • Total area = 27 square centimeters + 6 square centimeters = 33 square centimeters

Therefore, the total area of the piece of jewelry is 33 square centimeters.