Triangle Area with Median: Finding Area of ADC when ABC = 32

Question

In front of you the next triangle:

Since AD is the median

Since the area of the triangle ABC is equal to 32.

Find the area of the triangle ADC.

Video Solution

Solution Steps

00:09 Let's find the area of triangle A D C.

00:13 A D is a median. Remember, a median divides a side into two equal parts.

00:19 So, it splits the triangle into two smaller triangles with equal areas.

00:26 The area of triangle A B C is the sum of the areas of the smaller triangles.

00:36 Plug in the given area values and solve step by step.

00:57 And that's how you find the solution!

Step-by-Step Solution

To solve this problem, we'll use the property that a median of a triangle divides it into two triangles of equal area. Given the area of $\triangle ABC$ is 32:

Since $AD$ is the median, it divides $\triangle ABC$ into two triangles $\triangle ABD$ and $\triangle ADC$ of equal area.
Thus, the area of $\triangle ADC = \frac{1}{2} \times \text{Area of } \triangle ABC = \frac{1}{2} \times 32 = 16.$

Therefore, the area of triangle $\triangle ADC$ is $16$ .

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