The area of `Delta ABC` is 44 ` cm^(2)` . If D is the midpoint of BC and E is the midpoint of AB, then the area ( in ` cm^2`) of ` DeltaBDE` is :

Options

A. `5.5`
B. `22`
C. `11`
D. `44`

Answer

To find the area of triangle BDE given that the area of triangle ABC is 44 cm², and D and E are midpoints of sides BC and AB respectively, we can follow these steps:

### Step 1: Understand the triangle and midpoints
We have triangle ABC with area 44 cm². D is the midpoint of side BC, and E is the midpoint of side AB.

**Hint:** Remember that midpoints divide the segments into equal halves.

### Step 2: Divide triangle ABC into two smaller triangles
Since D is the midpoint of BC, line AD divides triangle ABC into two smaller triangles: ABD and ACD. Because D is the midpoint, the areas of triangles ABD and ACD are equal.

**Calculation:**
Area of triangle ABD = Area of triangle ACD = Total area of triangle ABC / 2
Area of triangle ABD = 44 cm² / 2 = 22 cm²

**Hint:** When a line is drawn from a vertex to the midpoint of the opposite side, it divides the triangle into two triangles of equal area.

### Step 3: Analyze triangle ABD
Now, we focus on triangle ABD. E is the midpoint of side AB. Therefore, line segment DE divides triangle ABD into two smaller triangles: ADE and BDE. Since E is the midpoint, triangles ADE and BDE also have equal areas.

**Calculation:**
Area of triangle ADE = Area of triangle BDE = Area of triangle ABD / 2
Area of triangle BDE = 22 cm² / 2 = 11 cm²

**Hint:** Midpoints also divide the area of triangles into equal parts.

### Step 4: Conclusion
Thus, the area of triangle BDE is 11 cm².

**Final Answer:** The area of triangle BDE is 11 cm².