Awater trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides.
the exterior surface area of the trough is
the volume of the trough is
if a trough is emptied until the water level is even with the midsegment of the trapezoidal ends there will be cubic feet of water left in the trough.

Part a) The exterior surface area is equal to

Part b) The volume is equal to

Part c) The volume water left in the trough will be

Step-by-step explanation:

Part a) we know that

The exterior surface area is equal to the area of both trapezoids plus the area of both rectangles

so

Find the area of two rectangles

Find the area of two trapezoids

Applying Pythagoras theorem calculate the height h

substitute the value of h to find the area

The exterior surface area is equal to

Part b) Find the volume

We know that

The volume is equal to

where

B is the area of the trapezoidal face

L is the length of the trough

we have

substitute

Part c)

step 1

Calculate the area of the trapezoid for h=2 ft (the half)

the length of the midsegment of the trapezoid is (8+2)/2=5 ft

step 2

Find the volume

The volume is equal to

where

B is the area of the trapezoidal face

L is the length of the trough

we have

substitute

step-by-step explanation: