Given: Length of the prism = 80cm

Height of trapezium base = 10cm

Shorter side of trapezium base = 50cm

Larger side of trapezium base = 75cm

Cost of painting = 100 rupees per square meter

To find: cost to paint the water trough from inside and outside

Procedure:

As it is the water trough, we will have only 5 sides to be painted from both sides.

From, the figure we can see that, the trough lies on the shorter side of the trapezium, so the side of prism which has the longer edge of the trapezium in it is absent, we will not consider it.

So, the area to be painted will be 2 × (area of both bases + area of 3 faces of the prism)

Now we have to find the length of non-parallel side of the prism.

ie. here length (AD)

⇒ So, by Pythagoras theorem, we have AD² = AE² + ED²

⇒ AE = (75-50) = 12.5cm

⇒ AD² = (12.5)² + 10²

⇒ AD² = 156.25 + 100

= 256.25

SO, AD = √256.25

AD = 16cm

Here, we multiplied the area by 2 because we have to paint the prism from inside as well as outside.

So, area of prism to be painted = 2× (2× (area of trapezium) + (100×50)+(100×16) +(100×16))

⇒ area of prism to be painted = 2× (2×(10×) + (100×50)+(100×16) +(100×16))

⇒ area of prism to be painted = 2×(1250 + 5000 + 1600 + 1600)

⇒ area of prism to be painted = 18900cm² = 1.89m²

∴ cost of painting = area × cost per meter square

= 1.89m²× 100

= 189 rupees.

∴ cost of painting the trough from inside and outside is 189 rupees.