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cricket20 [7]
3 years ago
9

Find the area of following rhombuses. Round your answers to the nearest tenth if necessary.

Mathematics
1 answer:
polet [3.4K]3 years ago
7 0

Answer:

Area =55.4ft^2

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

\tan(60) = \frac{4\sqrt 3}{x}

Solve for x

x = \frac{4\sqrt 3}{\tan(60)}

\tan(60) = \sqrt 3

So:

x = \frac{4\sqrt 3}{\sqrt 3}

x = 4

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

Base = 4\sqrt 3

Height = 4

So, the area of the rhombus is 4 times the area of 1 triangle

Area = 4 * \frac{1}{2} * Base * Height

Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4

Area =2 * 4\sqrt 3 * 4

Area =55.4ft^2

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