In a triangle ABC, D is the midpoint of BC and E is the midpoint of AD. if area of triangle ABC is 144 meter square then find the area of triangle DCE
lots of 2:1 ratios,
triangle DCE = 1/4 triangle ABC
= (1/4)(144) = 36 m^2
To find the area of triangle DCE, we can use the fact that the area of a triangle is half the product of its base and height.
First, let's determine the base of triangle DCE. Since D is the midpoint of BC, BD and DC are equal in length. Therefore, the base of triangle DCE is DC.
Next, let's find the height of triangle DCE. Notice that E is the midpoint of AD, and DE is parallel to AC (since DE and AC are both lines passing through D). Therefore, the height of triangle DCE is equal to the height of triangle ABC.
Given that the area of triangle ABC is 144 square meters, we can find the height of triangle ABC by using the formula: area = (base * height) / 2. Plugging in the area as 144 square meters and rearranging the formula, we get: height = (area * 2) / base.
Since we already know the base of triangle DCE is DC, we can use this formula to find the height of triangle ABC. Once we have the value for the height, we can use it to find the area of triangle DCE, which is equal to (DC * height) / 2.
Therefore, to find the area of triangle DCE:
1. Determine the base of triangle DCE, which is DC (same as BD).
2. Use the formula: height = (area of triangle ABC * 2) / base.
3. Calculate the height of triangle ABC using the given area of 144 square meters and the base DC.
4. Use the formula: area of triangle DCE = (DC * height of triangle ABC) / 2.