Предмет: Геометрия, автор: OneTheGod1

Знайти площу ромба, якщо один з його кутів на 90°більше за други а периметр дорівнює 28 корінь з 2

Приложения:

Ответы

Автор ответа: zmeura1204

Ответ:

Площа ромба дорівнює 49√2 см²

Объяснение:

Нехай градусна міра одного кута буде х°, а другого (х+90)°. Сума кутів прилеглих до однієї сторони ромба дорівнює 180°

Рівняння:

х+(х+90)=180

2х=180-90

х=90/2

х=45° гострий кут ромба.

Р=4а;

а=Р/4=28√2/4=7√2 см сторона ромба.

S=a²*sin∠x=(7√2)²*cos45°=

=49*2*√2/2=49√2 см²

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