Предмет: Геометрия, автор: buhs2

Сторона ромба равна 15 см, а одна из диагоналей 24 см. Найдите площадь
ромба.

Ответы

Автор ответа: Аноним
0

Пусть d_1,~d_2 - диагонали ромба, a - сторона ромба.

Сумма квадратов диагоналей ромба равна сумме квадратов его сторон

mathrm{d_1^2+d_2^2=4a^2~~Rightarrow~~\ d_2=sqrt{4a^2-d_1^2} =sqrt{4cdot 15^2-24^2} =18} см.

Площадь ромба равна 1/2 на произведение двух диагоналей.

displaystyle mathrm{S=dfrac{d_1cdot d_2}{2}=frac{24cdot18}{2}=216} см²

Ответ: 216 см².

Автор ответа: Санечка69
0

См. решение на рисунке

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