The quadrilateral

The quadrilateral ABCD is composed of two right triangles ABD and BCD. For side lengths: |AD| = 3cm, | BC | = 12cm, | BD | = 5cm. How many square centimeters (area) does the quadrilateral ABCD have? The angles DAB and DBC are right.

Correct answer:

S =  36 cm²

Step-by-step explanation:

$$\begin{gathered} AD=3\text{ cm } \\ BC=12\text{ cm } \\ BD=5\text{ cm } \\ AB=\sqrt{B{D}^2-A{D}^2}=\sqrt{5^2-3^2}=4\text{ cm } \\ {S}_1={\displaystyle \frac{AD\cdot AB}{2}}={\displaystyle \frac{3\cdot 4}{2}}=6{\text{cm}}^2 \\ {S}_2={\displaystyle \frac{BD\cdot BC}{2}}={\displaystyle \frac{5\cdot 12}{2}}=30{\text{cm}}^2 \\ S=S_1+S_2=6+30=36{\text{cm}}^2 \end{gathered}$$

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