# Pyramid

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

Result

S =  215.55 cm2

#### Solution:

$a=6 \ \text{cm} \ \\ b=8 \ \text{cm} \ \\ s=12.5 \ \text{cm} \ \\ \ \\ v_{1}=\sqrt{ s^2-(a/2)^2 }=\sqrt{ 12.5^2-(6/2)^2 } \doteq 12.1347 \ \text{cm} \ \\ v_{2}=\sqrt{ s^2-(b/2)^2 }=\sqrt{ 12.5^2-(8/2)^2 } \doteq 11.8427 \ \text{cm} \ \\ S_{1}=a \cdot \ v_{1}/2=6 \cdot \ 12.1347/2 \doteq 36.404 \ \text{cm}^2 \ \\ S_{2}=b \cdot \ v_{2}/2=8 \cdot \ 11.8427/2 \doteq 2 \ \sqrt{ 561 } \ \text{cm}^2 \doteq 47.3709 \ \text{cm}^2 \ \\ S_{3}=a \cdot \ b=6 \cdot \ 8=48 \ \text{cm}^2 \ \\ S=2 \cdot \ S_{1}+2 \cdot \ S_{2}+S_{3}=2 \cdot \ 36.404+2 \cdot \ 47.3709+48 \doteq 215.5497 \doteq 215.55 \ \text{cm}^2$

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