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.
Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?
Apologies for the error. Let's recalculate the areas of the triangles with the correct base and height measurements.
Area of each triangle:
Base = 2 cm
Height = 3 cm (for the top triangle) and 3 cm (for the bottom triangle)
Area = 1/2 x base x height
Area of top triangle:
Area = 1/2 x 2 cm x 3 cm
Area = 3 cm²
Area of bottom triangle:
Area = 1/2 x 2 cm x 3 cm
Area = 3 cm²
Now, let's calculate the total area of the piece of jewelry with the corrected triangle areas:
Total area = area of rectangle + 2 x area of triangle
Total area = 27 cm² + 3 cm² + 3 cm²
Total area = 33 cm²
Therefore, the total area of the piece of jewelry is 33 cm².
Wrong, the base of the triangle is 2 and the height is 3.
To find the total area of the piece of jewelry, we first need to find the individual areas of the rectangle and the two triangles, and then add them up.
Area of rectangle:
Length = 9 cm
Width = 3 cm
Area = length x width
Area = 9 cm x 3 cm
Area = 27 cm²
Area of each triangle:
Base = 2 cm
Height = 3 cm (for the top triangle) and 6 cm (for the bottom triangle)
Area = 1/2 x base x height
Area of top triangle = 1/2 x 2 cm x 3 cm
Area of top triangle = 3 cm²
Area of bottom triangle = 1/2 x 2 cm x 6 cm
Area of bottom triangle = 6 cm²
Total area of the piece of jewelry:
Total area = area of rectangle + 2 x area of triangle
Total area = 27 cm² + 3 cm² + 6 cm²
Total area = 36 cm²
Therefore, the total area of the piece of jewelry is 36 cm².