help_outlineУсловие задачи
Реши задачу: «Архитектурный эскиз: фасад здания из четырёхугольников» Суть: создать эскиз фасада здания, используя только четырёхугольники разных видов (прямоугольники, ромбы, трапеции). Задачи: нарисовать эскиз (от руки или в графическом редакторе); подписать размеры всех элементов; вычислить площадь каждого четырёхугольника и общую площадь фасада; придумать, как можно уменьшить площадь остекления на 20 % (изменить размеры окон‑прямоугольников), и пересчитать. Результат: рисунок + таблица с размерами и площадями + краткое объяснение изменений.
lightbulbКраткий ответ
Представлен пример архитектурного эскиза фасада здания, выполненного из различных четырёхугольников. Рассчитана площадь каждого элемента и предложены способы уменьшения площади остекления.
Вот решение вашей задачи по созданию архитектурного эскиза фасада здания из четырёхугольников.
Начнём с рисунка, затем перейдём к расчётам и объяснениям.
1. Эскиз фасада здания
Представим себе простой фасад здания. Для удобства расчётов и перерисовки, я опишу его словами, а вы сможете легко нарисовать его в тетради.
Представьте прямоугольный фасад здания.
* В центре фасада расположена большая входная группа, состоящая из прямоугольной двери и двух узких прямоугольных окон по бокам.
* Над входной группой, на втором этаже, расположено большое прямоугольное окно.
* По бокам от центральной части, на первом и втором этажах, расположены по два окна: одно прямоугольное и одно в форме трапеции.
* Крыша здания имеет форму трапеции (если смотреть на фасад).
Давайте зададим размеры для всех элементов.
Размеры элементов фасада:
* Общий фасад:
* Ширина: 12 м
* Высота (до начала крыши): 8 м
* Крыша (трапеция):
* Нижнее основание: 12 м (совпадает с шириной фасада)
* Верхнее основание: 8 м
* Высота: 3 м
* Входная группа (центр):
* Дверь (прямоугольник):
* Ширина: 2 м
* Высота: 2.5 м
* Боковые окна у двери (2 прямоугольника):
* Ширина: 0.5 м
* Высота: 2 м
* Расстояние от двери до окна: 0.25 м (с каждой стороны)
* Центральное окно 2-го этажа (прямоугольник):
* Ширина: 3 м
* Высота: 2 м
* Расположено по центру фасада, на высоте 4 м от земли.
* Боковые окна 1-го этажа (слева и справа от центра):
* Прямоугольное окно:
* Ширина: 1.5 м
* Высота: 1.5 м
* Расположено на расстоянии 1 м от края фасада и 1 м от земли.
* Трапециевидное окно:
* Нижнее основание: 1.5 м
* Верхнее основание: 1 м
* Высота: 1.5 м
* Расположено между прямоугольным окном и центральной частью, на высоте 1 м от земли.
* Боковые окна 2-го этажа (слева и справа от центра):
* Прямоугольное окно:
* Ширина: 1.5 м
* Высота: 1.5 м
* Расположено на расстоянии 1 м от края фасада и 4 м от земли.
* Трапециевидное окно:
* Нижнее основание: 1.5 м
* Верхнее основание: 1 м
* Высота: 1.5 м
* Расположено между прямоугольным окном и центральной частью, на высоте 4 м от земли.
2. Вычисление площади каждого четырёхугольника и общей площади фасада
Для вычислений будем использовать следующие формулы:
* Площадь прямоугольника: \(S = a \cdot b\)
* Площадь трапеции: \(S = \frac{a+b}{2} \cdot h\)
Таблица с размерами и площадями элементов фасада
| Элемент фасада | Тип четырёхугольника | Размеры | Площадь (\(м^2\)) |
| :-------------------------------- | :-------------------- | 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