In an isosceles trapezoid ABCD, the height lowered from the top to the larger base AD is 4cm and divides

In an isosceles trapezoid ABCD, the height lowered from the top to the larger base AD is 4cm and divides AD into segments equal to 5cm and 9cm What is the area of the trapezoid

Determine the length of the larger base of the trapezoid. AD = AH + DH = 14 cm.

Let’s draw the second height of the CD trapezoid. Since, according to the condition, the trapezoid is isosceles, then the right-angled triangles ABН and CDM are equal in hypotenuse and acute angle, then DM = AH = 5 cm.

Segment НМ = АD = АН – DM = 14 – 5 – 5 = 4 cm.

Quadrangle BCMН is a rectangle, then BC = НM = 4 cm.

Determine the area of the trapezoid.

Str = (ВС + АD) * ВН / 2 = (4 + 14) * 4/2 = 36 cm2.

Answer: The area of the trapezoid is 36 cm2.