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

June 26, 2021 | education

| 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.