Find the lateral and surface area of the right rectangular prism whose length is 7 cm, width is 5 cm, and height is 1.5 cm. I got 36 as my lateral area and 106 as my surface area. Is this right?
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To find the lateral area of a right rectangular prism, you need to calculate the sum of the areas of its four lateral faces. The formula for the lateral area of a rectangular prism is given as:
Lateral Area = 2 * (length * height + width * height)
Substituting the given values into the formula:
Lateral Area = 2 * (7 cm * 1.5 cm + 5 cm * 1.5 cm)
= 2 * (10.5 cm² + 7.5 cm²)
= 2 * 18 cm²
= 36 cm²
So, your calculation of 36 cm² for the lateral area is correct.
Next, to find the surface area of a right rectangular prism, you need to calculate the sum of the areas of all its six faces. The formula for the surface area is given as:
Surface Area = 2 * (length * width + length * height + width * height)
Substituting the given values into the formula:
Surface Area = 2 * (7 cm * 5 cm + 7 cm * 1.5 cm + 5 cm * 1.5 cm)
= 2 * (35 cm² + 10.5 cm² + 7.5 cm²)
= 2 * 53 cm²
= 106 cm²
So, your calculation of 106 cm² for the surface area is also correct.
Therefore, your calculations for both the lateral area and surface area of the right rectangular prism are correct: Lateral Area = 36 cm² and Surface Area = 106 cm². Well done!
To find the lateral and surface area of a right rectangular prism, you can use the following formulas:
Lateral Area = 2h(l + w)
Surface Area = 2lw + 2lh + 2wh
Given that the length (l) is 7 cm, the width (w) is 5 cm, and the height (h) is 1.5 cm, let's plug these values into the formulas and calculate:
Lateral Area = 2 * 1.5 cm * (7 cm + 5 cm) = 2 * 1.5 cm * 12 cm = 36 cm²
Surface Area = 2 * 7 cm * 5 cm + 2 * 7 cm * 1.5 cm + 2 * 5 cm * 1.5 cm = 70 cm² + 21 cm² + 15 cm² = 106 cm²
So, your calculations are correct. The lateral area is 36 cm², and the surface area is 106 cm².