Triangle Area Calculation: Using Median AD to Find Area of Triangle ABC from Area 15

Question

In front of you the next triangle:

Since AD is the median

Since the area of the triangle ADB is equal to 15.

Find the area of the triangle ABC.

Video Solution

Solution Steps

00:00 Determine the area of triangle ABC

00:03 AD is a median according to the given data, a median bisects the side

00:17 The median to a side in a triangle creates two triangles of equal area

00:24 Substitute in the area value according to the given data

00:31 The area of triangle ABC equals the sum of the areas of the triangles within it

00:43 This is the solution

Step-by-Step Solution

To solve this problem, we'll employ the theorem which states that the median of a triangle divides it into two triangles of equal area. Given that $AD$ is a median of $\triangle ABC$ , it divides $\triangle ABC$ into $\triangle ADB$ and $\triangle ADC$ .

Step 1: Recognize the properties of a median. The median $AD$ implies:
- Area of $\triangle ADB =$ Area of $\triangle ADC$ .
- Given Area of $\triangle ADB = 15$ , hence Area of $\triangle ADC = 15$ .

Step 2: Compute the total area of $\triangle ABC$ :
- Total Area of $\triangle ABC =$ Area of $\triangle ADB +$ Area of $\triangle ADC = 15 + 15 = 30.$

Thus, the area of triangle $\triangle ABC$ is $\boxed{30}$ .

Answer

Related Subjects

The Sum of the Interior Angles of a Triangle The sides or edges of a triangle Triangle Height Exterior angles of a triangle Median in a triangle Center of a Triangle - The Centroid - The Intersection Point of Medians All terms in triangle calculation