Question

Найдите сторону и площадь ромба, если его диагонали 6 и8 см​

Answer 1

Ответ:

$s = \frac{1}{2} {d}^{1} \times {d}^{2}$

S= 24

Answer 2

Finding the Side and Area of a Rhombus

To find the side and area of a rhombus when its diagonals are 6 and 8 cm, we can use the following formulas:

1. Side of the Rhombus (s): - The side of the rhombus can be calculated using the formula: \( s = \sqrt{\frac{d1^2 + d2^2}{4}} \), where \( d1 \) and \( d2 \) are the lengths of the diagonals.

2. Area of the Rhombus (A): - The area of the rhombus can be calculated using the formula: \( A = \frac{d1 \times d2}{2} \), where \( d1 \) and \( d2 \) are the lengths of the diagonals.

Let's calculate the side and area of the rhombus using the given diagonals.

Calculations

1. Side of the Rhombus: - Using the formula \( s = \sqrt{\frac{d1^2 + d2^2}{4}} \), where \( d1 = 6 \) cm and \( d2 = 8 \) cm: - \( s = \sqrt{\frac{6^2 + 8^2}{4}} \) - \( s = \sqrt{\frac{36 + 64}{4}} \) - \( s = \sqrt{\frac{100}{4}} \) - \( s = \sqrt{25} \) - s = 5 cm

2. Area of the Rhombus: - Using the formula \( A = \frac{d1 \times d2}{2} \), where \( d1 = 6 \) cm and \( d2 = 8 \) cm: - \( A = \frac{6 \times 8}{2} \) - \( A = \frac{48}{2} \) - A = 24 sq. cm

So, for a rhombus with diagonals of 6 cm and 8 cm, the side length is 5 cm and the area is 24 sq. cm.