On the 12 cm side AB of square ABCD, point E is marked so that CE = 13 cm. Find the area of the quadrilateral AECD.

The resulting quadrilateral AECD is a rectangular trapezoid. The area of the trapezoid is equal to the half-sum of the bases multiplied by the height of the trapezoid. To find the area ACED, you need to find the base of the trapezoid AE.

Let’s find the leg EB of the right-angled triangle EBU according to the Pythagorean theorem:

a² + b² = c²;

EB² + BC² = EC²;

EB² + 12² = 13²;

EB² + 144 = 169;

EB² = 25;

EB = 5 cm.

AE = AB – EB;

AE = 12 – 5 = 7 cm.

Find the area of the trapezoid AECD:

S = 1/2 * h * (a + b);

S = 1/2 * 12 * (12 + 7);

S = 6 * 19;

S = 114 cm².

Answer: 114 cm²