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QUESTION 1
Locate the centroid of the plane area shown if h = 15 in. Round the final answer to two decimal
places.
We find the area of the shaded area by first dividing it into two shapes; a triangle and a rectangle.
𝐴1 = 6 ∗ 3 = 18𝑖𝑛2
𝐴2 =
6
1
1
∗ ℎ ∗ 12 = ∗ 15 ∗ 12 = 90𝑖𝑛2
2
2
3
Centroid of 𝐴1 = (6 + 2 , ℎ + 2) = (9,16.5)
1
3
Centroid of a right angle triangle is at a distance of ∗ 𝑏 𝑎𝑛𝑑
1
Centroid of 𝐴2 along x-axis, 3 ∗ 12 = 4𝑖𝑛
1
3
∗ ℎ from the angle, therefore;
1
2
2
Along y-axis, ℎ − 3 ∗ ℎ = 3 ℎ = 3 ∗ 15 = 10𝑖𝑛
Centroid of 𝐴2 = (4,10)
To find the centroid of the shaded area, we use area moments. Moment at the centroid is zero.
Let 𝑥 and 𝑦 be the points of the centroid along x-axis and y-axis respectively.
Moments along y-axis,
(18 ∗ 9) + (90 ∗ 4) = 𝐴 ∗ 𝑥
Where 𝐴 is the total area, 𝐴1 + 𝐴2
162 + 360 = (90 + 18) ∗ 𝑥
Simplifying,
𝑥=
162 + 360 522
=
= 4.83𝑖𝑛
(90 + 18) 108
Moments along x-axis,
(18 ∗ 16.5) + (90 ...