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gmany gmany · Answer 1 · 2018-12-08T21:08:59+01:00

The base is an equilateral triangle. The formula of the area of that triangle is:

[tex]A=\dfrac{a^2\sqrt3}{4}[/tex]

a - length of side

a = 3". Substitute:

[tex]A_B=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}[/tex]

The lateral side is a rectangle.

[tex]A_{LS}=3\cdot6=18[/tex]

The Total Area is equal the sum of two times of Base and three times of Lateral Side.

[tex]T.A.=2\cdot\dfrac{9\sqrt3}{4}+3\cdot18=\dfrac{9\sqrt3}{2}+54\\\\\boxed{Answer:\ T.A.=54+4.5\sqrt3}[/tex]

jbiain jbiain · Answer 2 · 2019-11-28T14:57:43+01:00

Answer:

[tex]T.A. = 18 + \frac{9}{4}\sqrt{3} [/tex]

Step-by-step explanation:

The figure can be decomposed in an equilateral triangle, with sides = 3'', and a rectangle with sides 3'' and 6''.

The area of an equilateral triangle (A1) is calculated as follows:

[tex]A1 = \frac{a^2 \sqrt{3}}{4} [/tex]

where a refers to the length of each side of the triangle. Here a = 3. Replacing:

[tex]A1 = \frac{3^2 \sqrt{3}}{4} [/tex]

[tex]A1 = \frac{9}{4}\sqrt{3} [/tex]

The area of the rectangle is: 3*6 = 18'' = A2

The total area (T.A) is the addition of A1 to A2, So:

[tex]T.A. = 18 + \frac{9}{4}\sqrt{3} [/tex]

Notice that the line after after the + sign is not a subtract symbol, it is the line between numerator and denominator of the answer