The bases of an isosceles trapezoid are 8 and 18, and its perimeter is 52. Find the area of the trapezoid.

the perimeter of an isosceles trapezoid is:
P = a + b + 2c,
where a is the smaller base, b is the larger base, c is the side.
Substitute the known values ​​and find the side length:
52 = 8 + 18 + 2s;
2c = 52 – 26;
2c = 26;
c = 26/2;
c = 13 conventional units.
The area of ​​an isosceles trapezoid can be found, knowing all its sides, by the formula:
S = 1/4 √ ((a + b) ^ 2 (a – b + 2c) (b – a + 2c)).
Substitute the known values ​​and find the area of ​​the trapezoid:
S = 1/4 √ ((8 + 18) ^ 2 (8 – 18 + 2 * 13) (18 – 8 + 2 * 13)) = 1/4 √ (26 ^ 2 (26 – 10) (26 + 10)) = 26/4 √ (26 ^ 2 – 10 ^ 2) = 13/2 √ (676 – 100) = 13/2 √576 = 13/2 * 24 = 13 * 12 = 156 (conventional square units) …
Answer: S = 156 conventional square units.