Question

these prisms are similar. find the surface area of the larger prism. round to the nearest tenth.

5 in.
surface area = \\(572\text{ m}^2\\)

6 in.
surface area = \\(\\ ?\\ \text{ m}^2\\)

Explanation:

Identify the scale factor of the similar prisms

Using the Similar Solids knowledge point

$$ k = \frac{6\text{ in.}}{5\text{ in.}} = 1.2 $$

Set up the surface area ratio relation

Using the Surface Area Ratio knowledge point

$$ \frac{\text{SA}_{\text{larger}}}{\text{SA}_{\text{smaller}}} = k^2 = (1.2)^2 = 1.44 $$

Calculate the surface area of the larger prism

Using the Surface Area Ratio knowledge point

$$ \text{SA}_{\text{larger}} = 572 \times 1.44 = 823.68 $$

Round to the nearest tenth

Using the Surface Area Ratio knowledge point

$$ \text{SA}_{\text{larger}} \approx 823.7 $$

Answer:

These prisms are similar. Find the surface area of the larger prism. Round to the nearest tenth.

Surface Area = <blank>823.7</blank> \(\text{m}^2\)