Answer: 15 cm²
Step-by-step explanation:
Let x represent the length of the base of the smaller right angle triangle (drawn in broken lines).
The base of the full triangle would be (10 + x) cm. To determine x, we would apply the Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
12² = 3² + (10 + x)²
144 = 9 + (10 + x)²
(10 + x)² = 144 - 9 = 135
Taking square root of both sides
10 + x = √135 = 11.62
x = 11.62 - 10
x = 1.62
The total base of the triangle is 11.62cm
The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
Area of the full triangle is
Area = 1/2 × 11.62 × 3 = 17.43 cm²
Area of the smaller triangle (with broken lines) is
Area = 1/2 × 1.62 × 3 = 2.43 cm²
Area of the given figure is
17.43 - 2.43 = 15 cm²
