Respuesta :

baabaagreysheep

Your answer is L = 11 cm.

If the volumes of both shapes are the same, then we can set them equal to each other and solve for L to find the answer.

The volume of a rectangular prism is base × height × depth, which comes to 5 × 6 × L = 30L

The volume of the trapezoid prism (the shape on the left) would be the area of the trapezoid on the front, multiplied by the depth. This gives you:

[tex]\frac{7 + 4}{2}[/tex] × 6 × 10 = 5.5 × 6 × 10 = 330

So now we get:

330 = 30L

÷ 30

L = 11

I hope this helps!

S1NGH

Answer:

L = 11

Step-by-step explanation:

We are presented with a cuboid and a trapezoidal prism. Since we know that the two shapes have the same volume we should work out the volume of the trapezoidal prism to then guide us with working out the volume of the cuboid.

→ Let's first work out the volume of the trapezoidal prism

We should work out the area of the front face of the trapezium so we are going to utilise the formula  [tex]\frac{1}{2}[/tex] × ( a + b ) × h

Where 'a' and 'b' are the parallel sides and 'h' is the height

Area =  [tex]\frac{1}{2}[/tex] × ( 7 + 4 ) × 6  

Area of the front face = 33 cm²

Now we multiply that length by the 10 so,

33 × 10 = 330

We can use that value to help us work out the missing value for the cuboid

5 × 6 × L = 330

→ Simplify

30 × L = 330

→ Divide both sides by 30 to isolate L

L = 11

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