Quadrilateral-trapezoid 3172

We cut two triangles from the rectangular plate so that the resulting quadrilateral-trapezoid with the same arm lengths has an area of 32 cm², and one of its bases is twice as long as the other. What is the area of the two triangles that make up the waste?

Correct answer:

S =  10.6667 cm²

Step-by-step explanation:

$$\begin{gathered} a=2c \\ 32=(a+c)h/2 \\ S=ah-32 \\ 64=(a+a/2)h \\ 128=3ah \\ ah=128/3 \\ {S}_1=128/3=\frac{128}{3}\doteq 42.6667 \\ S=S_1-32 \\ S=S_1-32=42.6667-32=10.6667{\text{cm}}^2 \end{gathered}$$

Try another example