Question

Абажур правильной четырехугольной усеченной пирамиды без оснований изготовлен из ткани. Хватит ли отрезка ткани в форме квадрата со стороной 50 см. для изготовления этого абажура? Стороны: 8см, 26см, 28см

Answer 1

AM=ad-bc/2=28-8/2=10cm
по теореме пифагора.
вм=24см
ответ. хватит квадрат 50на50

Answer 2

Calculating Fabric Requirement for a Lampshade

To calculate whether a 50 cm square fabric is sufficient to make a lampshade for a correctly proportioned truncated square pyramid with the given dimensions (8 cm, 26 cm, 28 cm), we can use the formula for the lateral surface area of a truncated square pyramid.

The formula for the lateral surface area (A) of a truncated square pyramid is given by:

A = l * (s1 + s2 + sqrt(s1 * s2))

Where: - l is the slant height of the pyramid - s1 and s2 are the lengths of the parallel sides of the trapezoidal face

Let's calculate the lateral surface area using the given dimensions.

Calculating the Lateral Surface Area

Given: - s1 = 8 cm - s2 = 26 cm - l = 28 cm

Using the formula: A = 28 * (8 + 26 + sqrt(8 * 26))

Calculating the value: A ≈ 28 * (8 + 26 + sqrt(208)) A ≈ 28 * (8 + 26 + 14.42) A ≈ 28 * 48.42 A ≈ 1357.76 cm²

Evaluating the Fabric Requirement

Now, let's compare the calculated lateral surface area with the area of the 50 cm square fabric to determine if it's sufficient for making the lampshade.

The area of a 50 cm square fabric is: Area = 50 * 50 Area = 2500 cm²

As the calculated lateral surface area of the lampshade is approximately 1357.76 cm², it is evident that the 50 cm square fabric is more than sufficient to make the lampshade.