The diagonals of this rhombus are 8 and 16 units long. Their intersection creates four right angles, two 4-unit-long segments, and two 8-uni

Question

The diagonals of this rhombus are 8 and 16 units long. Their intersection creates four right angles, two 4-unit-long segments, and two 8-unit long segments. Given this information, find the area of the rhombus in square units (Use only the digits 0 – 9 and the decimal point, if needed, to enter a number).

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Vân Khánh 5 months 2021-08-20T17:54:55+00:00 1 Answers 0 views 0

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    2021-08-20T17:56:23+00:00

    Answer:

    64\ \text{sq. units}

    Step-by-step explanation:

    Area of a rhombus is the product of the length of the diagonals divided by two.

    Length of one diagonal is 8 units and the other diagonal is 16 units

    Area is given by

    A=\dfrac{8\times 16}{2}\\\Rightarrow A=64\ \text{sq. units}

    The area of the rhombus is 64\ \text{sq. units}

    Another approach is the diagonals have created 4 triangles where the base and is height is either 4 units long or 8 units long so the area of the rhombus would be the area of the 4 triangles.

    A=4\times \dfrac{1}{2}\times 4\times 8\\\Rightarrow A=64\ \text{sq. units}

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