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asambeis [7]
3 years ago
12

Big boy points for big boy question

Mathematics
2 answers:
Jobisdone [24]3 years ago
8 0

36 \sqrt{3}+ 72

The length of the rectangle = diameter of 2 circles = 4 × 3 = 12 mm

The width of the rectangle = 2 radii + distance d between radii ( lower to upper )

Using the right triangle formed by joining the 3 centres with legs 3 and d and hypotenuse 6

Using Pythagoras' identity, then

d² + 3² = 6²

d² + 9 = 36 ( subtract 9 from both sides )

d² = 27 ( take the square root of both sides )

d =  = 3

Thus width of rectangle = 3 + 3 + 3 = 6 + 3

Hence

area = length × width

       = 12 × (6 + 3 ) = 36 + 72 mm ²

trapecia [35]3 years ago
7 0

Answer:

36\sqrt{3} + 72

Step-by-step explanation:

The length of the rectangle = diameter of 2 circles = 4 × 3 = 12 mm

The width of the rectangle = 2 radii + distance d between radii ( lower to upper )

Using the right triangle formed by joining the 3 centres with legs 3 and d and hypotenuse 6

Using Pythagoras' identity, then

d² + 3² = 6²

d² + 9 = 36 ( subtract 9 from both sides )

d² = 27 ( take the square root of both sides )

d = \sqrt{27} = 3\sqrt{3}

Thus width of rectangle = 3 + 3\sqrt{3} + 3 = 6 + 3\sqrt{3}

Hence

area = length × width

        = 12 × (6 + 3\sqrt{3} ) = 36\sqrt{3} + 72 mm ²

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