Question

По стороне основания d=6 см и боковому ребру b=12 см правильной треугольной призмы определите площадь сечения проведенного через боковон ребро и ось призмы(с точностью до целых)

Answer 1

Сечение-прямоугольник,большая сторона=12,меньшая-высота в правильном треугольнике,который является основание призмы => h=кор(3)/2*6=3*кор(3) => S=12*3*кор(3)=62

Answer 2

Calculating the Cross-Sectional Area of a Prism

To calculate the cross-sectional area of the prism, we can use the formula:

Cross-sectional area = (base side length) * (height of the prism)

Given: - Base side length (d) = 6 cm - Side edge length (b) = 12 cm

We need to find the height of the prism to calculate the cross-sectional area.

Finding the Height of the Prism

To find the height of the prism, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the Pythagorean theorem: - c^2 = a^2 + b^2 - Where c is the hypotenuse (height of the prism), and a and b are the other two sides.

Given: - Base side length (d) = 6 cm - Side edge length (b) = 12 cm

We can calculate the height (c) using the formula: c = √(d^2 + b^2)

Calculating the Cross-Sectional Area

Now that we have the height of the prism, we can calculate the cross-sectional area using the formula: Cross-sectional area = (base side length) * (height of the prism)

Substitute the values: Cross-sectional area = 6 cm * (calculated height)

Let's calculate the height using the given values and then find the cross-sectional area.