Pyramid

The pyramid has a base rectangle with a = 6cm and b = 8cm. The side edges are the same, and their length is 12.5 cm. Calculate the surface of the pyramid.

Correct answer:

S =  215.5497 cm²

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ b=8\text{cm} \\ s=12.5\text{cm} \\ {v}_1=\sqrt{s^2-(a/2{)}^2}=\sqrt{12.5^2-(6/2{)}^2}\doteq 12.1347\text{cm} \\ {v}_2=\sqrt{s^2-(b/2{)}^2}=\sqrt{12.5^2-(8/2{)}^2}\doteq 11.8427\text{cm} \\ {S}_1=a\cdot v_1/2=6\cdot 12.1347/2\doteq 36.404{\text{cm}}^2 \\ {S}_2=b\cdot v_2/2=8\cdot 11.8427/2=2\sqrt{561}{\text{cm}}^2\doteq 47.3709{\text{cm}}^2 \\ {S}_3=a\cdot b=6\cdot 8=48{\text{cm}}^2 \\ S=2\cdot S_1+2\cdot S_2+S_3=2\cdot 36.404+2\cdot 47.3709+48=215.5497{\text{cm}}^2 \end{gathered}$$

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