Quadrilaterals

5 cm

Step 1: This is an application of the midpoint theorem. Step 2: The midpoint theorem states that the line joining midpoints of two sides of a triangle is parallel to the third side and half its length. Step 3: DE joins midpoints D and E of sides AB and AC. Step 4: Therefore, DE = (1/2) × BC = (1/2) × 10 = 5 cm.

Trapezium

Step 1: Let's analyze each option by their defining properties. Step 2: Parallelogram has both pairs of opposite sides parallel. Step 3: Rectangle and rhombus are special parallelograms, so they also have both pairs parallel. Step 4: Trapezium is defined as having exactly one pair of parallel sides, which matches the question.

24 cm²

Step 1: A diagonal of a parallelogram divides it into two triangles of equal area. Step 2: Diagonal AC divides parallelogram ABCD into triangles ABC and ACD. Step 3: Area of triangle ABC = Area of triangle ACD = (1/2) × Area of parallelogram. Step 4: Area of triangle ABC = (1/2) × 48 = 24 cm².

90°

Step 1: Sum of interior angles of a quadrilateral = 360°. Step 2: Let the fourth angle be x°. Step 3: 85° + 75° + 110° + x° = 360°. Step 4: 270° + x° = 360°, so x° = 360° - 270° = 90°.