Find the area of the following figure:

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