Triangle's 16613

They make bases for table lamps from bronze in the shape of an isosceles triangle. How many m² are needed for 5 mats if the arms are 24 cm long and the height to the triangle's base is 1.5 dm?

Correct answer:

S =  0.1405 m²

Step-by-step explanation:

$$\begin{gathered} n=5 \\ r=24\text{cm}\to \text{m}=24:100\text{m}=0.24\text{m} \\ h=1.5\text{dm}\to \text{m}=1.5:10\text{m}=0.15\text{m} \\ (a/2{)}^2=r^2-h^2={\frac{6}{25}}^2-{\frac{3}{20}}^2=0.0351 \\ a=2\cdot \sqrt{r^2-h^2}=2\cdot \sqrt{0.24^2-0.15^2}\doteq 0.3747\text{m} \\ {S}_1=\frac{a\cdot h}{2}=\frac{0.3747\cdot 0.15}{2}\doteq 0.0281{\text{m}}^2 \\ S=n\cdot S_1=5\cdot 0.0281=0.1405{\text{m}}^2 \end{gathered}$$

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