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

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

step-by-step explanation:

because it just is