Rectangular 5798

The pyramid has a rectangular base with dimensions a = 5cm, b = 6cm.
The side edges are identical; their length is h = 11cm.
Calculate the surface of the pyramid.

Correct answer:

S =  147.0587 cm²

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ b=6\text{cm} \\ s=11\text{cm} \\ {v}_1=\sqrt{s^2-(a/2{)}^2}=\sqrt{11^2-(5/2{)}^2}\doteq 10.7121\text{cm} \\ {v}_2=\sqrt{s^2-(b/2{)}^2}=\sqrt{11^2-(6/2{)}^2}=4\sqrt{7}\text{cm}\doteq 10.583\text{cm} \\ {S}_1=a\cdot v_1/2=5\cdot 10.7121/2\doteq 26.7804{\text{cm}}^2 \\ {S}_2=b\cdot v_2/2=6\cdot 10.583/2=12\sqrt{7}{\text{cm}}^2\doteq 31.749{\text{cm}}^2 \\ {S}_3=a\cdot b=5\cdot 6=30{\text{cm}}^2 \\ S=2\cdot S_1+2\cdot S_2+S_3=2\cdot 26.7804+2\cdot 31.749+30=147.0587{\text{cm}}^2 \end{gathered}$$

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