# In a right-angled isosceles triangle, the height is 3, find its area

1. Vertices of the triangle – A, B, C. ∠C = 90 °. AC = BC. Height CE = 3 units.

2. By the condition of the problem, the given triangle is isosceles. Therefore, ∠A = ∠B.

3. Considering that the sum of the interior angles of the triangle is 180 °, we calculate the degree measure of these angles:

∠А = ∠В = (180 ° – 90 °) / 2 = 45 °.

4. Calculate the length of the segment AE through the tangent ∠А:

CE / AE = tangent ∠A = tangent 45 ° = 1.

AE = CE: 1 = 3: 1 = 3 units.

AE = BE, since the height of CE, which is also the median, divides AB into two identical segments. That is, AE = BE = 3 units.

5. AB = AE + BE = 3 + 3 = 6 units.

6. Calculate the area (S) of a given triangle:

S = AB x CE / 2 = 6 x 3/2 = 9 units².

Answer: The area of a given triangle is 9 units of measurement².