Final answer:
To find the composite area of a half circle with a diameter of 4 cm and a rectangle with a length of 6 cm and a triangle with a side length of 4 cm, you can calculate the area of each shape separately and then add them together. The area of a half circle is (π * r^2) / 2, the area of a rectangle is length * width, and the area of a triangle is (1/2) * base * height.
Step-by-step explanation:
To find the composite area of a half circle and a rectangle with a triangle, we need to calculate the area of each shape separately and then add them together.
The area of a half circle with a diameter of 4 cm can be found using the formula A = (π * r^2) / 2.
Since the diameter is 4 cm, the radius is half of that, which is 2 cm.
Plugging in the values, we get
A = (π * 2^2) / 2
= 2π cm².
The area of a rectangle with a length of 6 cm is simply the product of its length and width. If the width is not given, we can assume it to be the same as the diameter of the half circle, which is 4 cm.
Thus, the area of the rectangle is 6 cm * 4 cm = 24 cm².
The area of a triangle can be found using the formula A = (1/2) * base * height.
Given that the side length of the triangle is 4 cm, we can assume it to be the base and the height to be the same.
Thus, the area of the triangle is
(1/2) * 4 cm * 4 cm = 8 cm².
To find the composite area, we simply add the areas of the three shapes together:
2π cm² + 24 cm² + 8 cm²
= (2π + 32) cm².