If M is the midpoint of CD and ABCD is trapezium in which ADIIBC, if the area of ABCM = 4 and the area of AMND = 6, then find the area of trapezium
ABCD. (Given N is the mid point of AD)

We are given a trapezium \( ABCD \) with the following information:

- \( M \) is the midpoint of \( CD \).
- \( N \) is the midpoint of \( AD \).
- \( AD \parallel BC \) (trapezium property).
- The area of \( ABCM \) is 4, and the area of \( AMND \) is 6.
- We need to find the total area of trapezium \( ABCD \).

### Step 1: Area Analysis
The total area of the trapezium \( ABCD \) can be thought of as the sum of two parts:
- The area of \( ABCM \) (which is given as 4).
- The area of \( AMND \) (which is given as 6).

Thus, the total area of trapezium \( ABCD \) can be found by adding these two areas:
\[
\text{Area of } ABCD = \text{Area of } ABCM + \text{Area of } AMND
\]
\[
\text{Area of } ABCD = 4 + 6 = 10
\]

Therefore, the area of trapezium \( ABCD \) is \( \boxed{10} \).

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Would you like more details on any part of the solution?

Here are some related questions for further practice:
1. How do you calculate the area of a trapezium given the lengths of parallel sides and height?
2. How does knowing the midpoints of sides help simplify area calculations in geometric shapes?
3. What is the difference between the area of a triangle and a trapezium?
4. If \( AB \parallel CD \), how does it affect the shape of \( ABCD \)?
5. How would the area change if \( AB \) and \( CD \) were of different lengths?

**Tip:** Always try breaking down complex shapes into simpler parts like triangles or quadrilaterals when calculating areas.

If M is the midpoint of CD and ABCD is trapezium in which AD || BC, if the area of ABCM = 4 and the area of AMND = 6, then find the area of trapezium ABCD. (Given N is the midpoint of AD)

Solve for the area of trapezium ABCD using midpoints M and N with areas of ABCM and AMND provided. Learn key geometric concepts including the Midpoint Theorem and area calculations in this step-by-step solution, ideal for students in Grades 8-10.

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