# Embankment

Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.

Result

S =  64.661 m2

#### Solution:

$h=4 \ \text{m} \ \\ c=7 \ \text{m} \ \\ r=10 \ \text{m} \ \\ x=\sqrt{ r^{ 2 }-h^{ 2 } }=\sqrt{ 10^{ 2 }-4^{ 2 } } \doteq 2 \ \sqrt{ 21 } \ \text{m} \doteq 9.1652 \ \text{m} \ \\ a=c + 2 \cdot \ x=7 + 2 \cdot \ 9.1652 \doteq 25.3303 \ \text{m} \ \\ S=(a+c) \cdot \ h/2=(25.3303+7) \cdot \ 4/2 \doteq 64.6606 \doteq 64.661 \ \text{m}^2$

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