Question

Сторона основи правильної трикутної призми дорівнює 12 см, а діагональбічної грані дорівнює 13 см.Знайти бічну поверхню призми.

Answer 1

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Answer 2

Given Information:

- Side length of the base of a right triangular prism = 12 cm - Diagonal of one of the faces of the prism = 13 cm

Finding the lateral surface area of the prism:

To find the lateral surface area of the prism, we need to calculate the sum of the areas of all the lateral faces.

The lateral surface area of a right triangular prism can be calculated using the formula: Lateral Surface Area = Perimeter of the base × Height

In this case, the base of the prism is a right triangle, and the height is the length of the diagonal of one of the faces.

To find the perimeter of the base, we need to calculate the sum of the lengths of all three sides of the right triangle. Since we only know the length of one side (12 cm), we need to find the lengths of the other two sides.

Using the Pythagorean theorem, we can find the lengths of the other two sides of the right triangle: a^2 + b^2 = c^2 where: - a and b are the lengths of the two sides of the right triangle - c is the length of the hypotenuse (diagonal of the face)

In this case, we know that the diagonal of the face is 13 cm. Let's solve for the lengths of the other two sides:

a^2 + b^2 = 13^2 a^2 + b^2 = 169

Since the triangle is a right triangle, one of the sides is perpendicular to the other. Therefore, we can assume that one side is the height of the triangle and the other side is the base of the triangle.

Let's assume that side a is the height and side b is the base. Solving the equation, we get:

a^2 + b^2 = 169 a^2 + 12^2 = 169 a^2 + 144 = 169 a^2 = 169 - 144 a^2 = 25 a = 5

Now that we know the lengths of all three sides of the right triangle, we can calculate the perimeter of the base:

Perimeter of the base = 12 + 5 + 13 = 30 cm

Finally, we can calculate the lateral surface area of the prism:

Lateral Surface Area = Perimeter of the base × Height = 30 cm × 13 cm = 390 cm^2

Therefore, the lateral surface area of the prism is 390 cm^2.

Answer:

The lateral surface area of the given right triangular prism is 390 cm^2.