Question

If the area of the triangle $ BGC $ is $ 28 $ square units and the centroid of the triangle is $ G $ . Then, find the area of the triangle $ ABC $ .

Answer 1

Hint: Use the properties of the centroid of triangle and also the property that the centroid of the triangle divides the triangle into three triangles of the equal area out of which one triangle is $ BGC $

Complete step-by-step answer:

As per the property of the centroid, the centroid divides the triangle into three triangles of equal area.
So, the triangle $ ABC $ is divided into three triangles $ ABG $ , $ ACG $ and $ BGC $ by the centroid $ G $ . All these three triangles are of equal area.
As given the area of the triangle $ BGC $ is $ 28 $ square units. So, the area of the triangles $ ABG $ , $ ACG $ is also equal to $ 28 $ square units each.
The total area of the triangle $ ABC $ is the sum of the area of the triangles $ ABG $ , $ ACG $ and $ BGC $ .
As the area of the triangles $ ABG $ , $ ACG $ and $ BGC $ is equal. So, the area of the triangle $ ABC $ is three times the area of the triangle $ BGC $ .
The area of triangle $ ABC $ is equal to $ 3 \times 28 = 84 $ square units.
So, the area of the triangle $ ABC $ is equal to $ 84 $ square units.
So, the correct answer is “ $ 84 $ square units”.

Note: The centroid is the intersection point of three of the median lines. The three medians also divide the triangle into six equal triangles which when combined in pairs of two gives three triangles of equal area.