What is the length of a diagonal and area of a rhombus, if the length of its side is 10 cm, and the length of the other diagonal
2 answers:
Answer:
The area of rhombus is 96 cm² and the length of other diagonal is 16 cm.
Step-by-step explanation:
Refer the figure given.
Using Pythagoras theorem to get half length of unknown diagonal
l =
Length of unknown diagonal = 2l = 2 x 8 = 16 cm
Area of rhombus is half of product of diagonals.
The side of a rhombus and the half-diagonals form a right triangle. The length of the other half-diagonal is found from the Pythagorean theorem to be
... d = √((10 cm)² -(6 cm)²) = √(64 cm²) = 8 cm
The length of the other diagonal is 16 cm.
The area is half the product of the diagonal lengths, so is
... area = (1/2)(12 cm)(16 cm) = 96 cm²
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