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Centroids Worksheet

Explore the concept of centroids, their calculation for various geometric shapes, and applications in this Grade 12 mathematics worksheet.

Grade 12 Math GeometryCentroids
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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSG.CO.C.10CCSS.MATH.CONTENT.HSG.GPE.B.7
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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)?

a

(3,2)

b

(6,4)

c

(0,0)

d

(3,4)

4. Calculate the centroid of the triangle with vertices A(1, 5), B(7, 2), and C(4, 9).

A(1,5)B(7,2)C(4,9)

5. The centroid of a triangle is always located inside the triangle.

T

True

F

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.)

(0,0)(8,0)(12,0)(8,6)(0,6)(10,4)