Centroids Worksheet
Explore the concept of centroids, their calculation for various geometric shapes, and applications in this Grade 12 mathematics worksheet.
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Centroids Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Define the term 'centroid' in the context of a geometric shape. How does it differ from the center of mass?
2. For a triangle with vertices (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (Cx, Cy) are given by the formulae: Cx = and Cy = .
3. What are the coordinates of the centroid of a rectangle with vertices at (0,0), (6,0), (6,4), and (0,4)?
(3,2)
(6,4)
(0,0)
(3,4)
4. Calculate the centroid of the triangle with vertices A(1, 5), B(7, 2), and C(4, 9).
5. The centroid of a triangle is always located inside the triangle.
True
False
6. A composite shape is formed by a rectangle with vertices (0,0), (8,0), (8,6), (0,6) and an isosceles triangle with vertices (8,0), (12,0), (10,4). Find the centroid of this composite shape. (Hint: Calculate the centroid and area of each individual shape first.)
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