Question

Боковое ребро правильной усеченной пирамиды равно 5 см, в основание лежат треугольники со сторонами 1 см и 9 см. Найдите площадь боковой поверхности это пирамиды

Answer 1

Боковая грань правильной усеченной пирамиды - равнобокая трапеция с основаниями а = 1 см, b = 9 см и боковой стороной с = 5 см.
Проведем высоты трапеции иp вершин меньшего основания на большее, которые разбивают его на отрезки  b = 1 + 8 + 1
В прямоугольном треугольнике с катетом 1 см, гипотенузой с = 5 см и неизвестным катетом h, по т. Пифагора
5² = 1² + h²
h = √24 = 2√6 (см) - высота трапеции 

Площадь трапеции с основаниями а = 1 см, b = 9 см и высотой h  = 2√6 см
S₁ = (1 + 9) * √6 = 10√6 (cm²)

В треугольной пирамиде три грани
S = 3S₁ = 30√6 (cm²)

Answer 2

Calculation of the lateral surface area of a truncated pyramid

To find the lateral surface area of a truncated pyramid, we need to know the length of the lateral edge and the lengths of the sides of the triangles in the base.

Given: - Length of the lateral edge = 5 cm - Sides of the triangles in the base = 1 cm and 9 cm

To calculate the lateral surface area, we can use the formula:

Lateral Surface Area = (Perimeter of the upper base + Perimeter of the lower base) * (Lateral edge length / 2)

Let's calculate the perimeter of the upper and lower bases first.

The perimeter of a triangle is the sum of its three sides. Since the triangles in the base have sides measuring 1 cm and 9 cm, the perimeter of each triangle is:

Perimeter of the triangle = 1 cm + 1 cm + 9 cm = 11 cm

Now, let's calculate the lateral surface area using the formula:

Lateral Surface Area = (Perimeter of the upper base + Perimeter of the lower base) * (Lateral edge length / 2)

Lateral Surface Area = (11 cm + 11 cm) * (5 cm / 2) = 22 cm * 2.5 cm = 55 cm²

Therefore, the lateral surface area of the given truncated pyramid is 55 cm².

Answer 3

Calculation of the lateral surface area of a truncated pyramid

To find the lateral surface area of a truncated pyramid, we need to know the length of the slant height and the perimeter of the bases.

Given information: - Length of the slant height (lateral edge) = 5 cm - Perimeter of the top base = 1 cm - Perimeter of the bottom base = 9 cm

To calculate the lateral surface area, we can use the formula:

Lateral Surface Area = (Perimeter of the top base + Perimeter of the bottom base) * (Length of the slant height) / 2

Let's substitute the given values into the formula:

Lateral Surface Area = (1 cm + 9 cm) * (5 cm) / 2

Simplifying the expression:

Lateral Surface Area = 10 cm * 5 cm / 2

Lateral Surface Area = 50 cm² / 2

Lateral Surface Area = 25 cm²

Therefore, the lateral surface area of the given truncated pyramid is 25 cm².