Math Problem Statement

resuelve

Hallar el área de superficie de este prisma rectangular.

Solution

To find the surface area of this rectangular prism, we’ll use the formula for the surface area of a rectangular prism:

Surface Area=2(l×w+l×h+w×h)\text{Surface Area} = 2(l \times w + l \times h + w \times h)

where:

  • ll is the length,
  • ww is the width, and
  • hh is the height.

From the image:

  • Length (ll) = 8 cm
  • Width (ww) = 5 cm
  • Height (hh) = 3 cm

Now, substitute these values into the formula:

Surface Area=2(8×5+8×3+5×3)\text{Surface Area} = 2(8 \times 5 + 8 \times 3 + 5 \times 3)

Calculate each part inside the parentheses:

  1. 8×5=408 \times 5 = 40
  2. 8×3=248 \times 3 = 24
  3. 5×3=155 \times 3 = 15

Now add these results:

40+24+15=7940 + 24 + 15 = 79

Finally, multiply by 2:

Surface Area=2×79=158 cm2\text{Surface Area} = 2 \times 79 = 158 \text{ cm}^2

So, the surface area of the prism is 158 cm².

Would you like further details or have any questions?

Here are some related questions to expand on this problem:

  1. What is the formula for the volume of a rectangular prism?
  2. How would the surface area change if the length were doubled?
  3. Can we find the surface area of a cube with the same edge length?
  4. How do you find the lateral surface area of a rectangular prism?
  5. What real-world objects resemble a rectangular prism in shape?

Tip: When calculating surface areas, carefully multiply each dimension pair separately before adding and doubling to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area Calculation

Formulas

Surface Area of a Rectangular Prism: 2(l × w + l × h + w × h)

Theorems

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Suitable Grade Level

Grades 5-7