In trapezoid ABCD base BC = 4 and AD = 9. It is known that AB = BC. Find the perimeter of the trapezoid.

1. It is known that:
AB = BC = 4;
AB = CD = 4.
2. Find the perimeter:
P = 4 + 4 + 4 + 9;
P = 21cm.
3. Let’s draw the heights H and K;
It turns out that ABH and KCD are equal in hypotenuse and acute angle, hence AH = KD.
In this way:
HK = BC = 4 cm;
AH = KD = 2.5 cm;
4. By the Pythagorean theorem, you need to find BH:
BH = 16 – 6.25;
BH = 9.75 cm.
5. Find the area:
S = 1/2 * (AD + BC) * BH;
S = 1/2 * (4 + 9) * 9.75;
S = 63.375 cm2.
Answer: P = 21cm.