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The problem described in the image is related to an isosceles trapezoid \( ABCD \), with the following properties:

- \( AB \parallel CD \) (AB and CD are parallel)
- \( AD = BC \) (the non-parallel sides are equal)
- \( AB = 24 \, \text{cm} \) (the larger base)
- \( AC \perp BC \) (diagonal \( AC \) is perpendicular to base \( BC \))

You are asked to calculate the following:

**a)** The area of the trapezoid \( ABCD \).

**b)** The distance from the vertex \( D \) to the side \( BC \).

**c)** The area of triangle \( MAB \), where \( M \) is the point where \( AD \) intersects \( BC \).

I will help you solve these one by one.

### Part a) Calculating the area of trapezoid \( ABCD \):

The area of an isosceles trapezoid is given by the formula:

\[
A = \frac{1}{2} \times (AB + CD) \times h
\]

Where:
- \( AB \) is the larger base.
- \( CD \) is the smaller base.
- \( h \) is the height, which can be calculated or derived from the problem.

To proceed further, I'll need information about either the height or the smaller base \( CD \), as they are not provided directly in the problem.

Do you have the value for \( CD \) or the height? If not, we can calculate them based on the perpendicular diagonal condition.

Trapeziul isoscel ABCD, cu AB || CD și AD = BC = DC, are baza mare AB = 24 cm și AC ⊥ BC. Calculați: a) aria trapezului ABCD; b) distanța de la vârful D la latura BC; c) aria triunghiului MAB, unde AD ∩ BC = {M}.

Solve the geometry problem involving the isosceles trapezoid ABCD with AB || CD, AD = BC = DC, and AC ⊥ BC. Calculate the area of the trapezoid, the distance from vertex D to BC, and the area of triangle MAB where AD intersects BC. This problem covers key concepts in geometry including trapezoid properties and distance calculations.

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