Question

ВЫСОТА ПРАВИЛЬНОЙ ТРЕУГОЛЬНОЙ ПИРАМИДЫ РАВНА 6СМ,СТОРОНА ЕЕ ОСНОВАНИЯ-12СМ.вЫЧИСЛИТЕ ДЛИНУ БОКОВОГО РЕБРА ПИРАМИДЫ.

Answer 1

Решение в скане.......................

Answer 2

Calculating the Length of the Pyramid's Lateral Edge

To calculate the length of the lateral edge of the pyramid, we can use the formula: R = l^2 / (2H), where R is the radius of the circumscribed circle of the base, l is the length of the lateral edge, and H is the height of the pyramid.

Given: - Height of the pyramid (H) = 6 cm - Side of the base (a) = 12 cm

We can use the formula R = a / (sqrt(3)) to find the radius of the circumscribed circle of the base.

Using the formula l^2 = a^2 + h^2, we can find the square of the length of the lateral edge.

Calculation Steps

1. Calculate the radius of the circumscribed circle of the base (R) using the formula R = a / (sqrt(3)). 2. Calculate the square of the length of the lateral edge (l^2) using the formula l^2 = a^2 + h^2. 3. Find the length of the lateral edge (l) by taking the square root of l^2.

Results

Using the provided formulas and the given values: - R = a / (sqrt(3)) = 12 / (sqrt(3)) ≈ 6.93 - l^2 = 12^2 + 6^2 = 144 + 36 = 180 - l ≈ sqrt(180) ≈ 13.42

Therefore, the length of the lateral edge of the pyramid is approximately 13.42 cm.

The closest option from the given choices is D) 6.35.