Perimeter of a quadrilateral ABCD is 120 cm. If BC = 48 cm, CD = 17 cm, AD =…

When two adjacent angles of a quadrilateral — the two angles at the two ends of one side — are both right angles, the two sides leaving those vertices at the other ends are both perpendicular to that shared side, and are therefore parallel to each other. Such a quadrilateral is a right trapezoid, and its area equals half the sum of the two parallel sides multiplied by the perpendicular distance between them (the shared side itself acts as the height).

1. Find AB using the perimeter: Perimeter = AB + BC + CD + AD, so 120 = AB + 48 + 17 + 40, giving AB = 120 − 105 = 15 cm.

2. Since ∠A = ∠B = 90°, both AD and BC are perpendicular to AB, so AD ∥ BC. ABCD is therefore a right trapezoid with parallel sides AD = 40 cm and BC = 48 cm, and height AB = 15 cm.

3. Area = ½ × (AD + BC) × AB = ½ × (40 + 48) × 15 = ½ × 88 × 15 = 44 × 15 = 660 cm2.

Placing A at the origin with AB along one axis — A(0,0), B(15,0), D(0,40), C(15,48) — gives CD = √((15−0)2 + (48−40)2) = √(225+64) = √289 = 17 cm, exactly matching the given CD. This confirms the construction and the area of 660 cm2.