This figure is made up of a rectangle and parallelogram. What is the area of this figure? Enter your answer in the box. Do not round any side lengths.

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This figure is made up of a rectangle and parallelogram. What is the area of this figure? Enter your answer in the box. Do not round any side lengths.

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Answer 1 · 2018-04-09T05:17:32

$Total Area of the given figure = 51 sq units$ $color(green)("Total Area of the given figure " = color(brown)(51 color(green)(" sq units"$

Explanation:

$T o f \in d A r e a o f P a r a l \leq log r a m A B C F & R e c tan g \leq C D E F$ $To find Area of Parallelogram ABCF & Rectangle CDEF"$

$Coordinates of A (4, - 9), B (7, - 7) C (- 3, 7), D (6, 1), E (4, - 2), F (- 5, 4), G (4, - 7)$ $"Coordinates of " A(4,-9), B(7,-7)C (-3, 7), D (6,1), E (4,-2), F (-5,4), G(4,-7)$

$A r e a o f p a r a l \leq log r a m A B C F = B C \cdot B G = 4 \cdot 3 = 12$ $"Area of parallelogram ABCF = BC * BG = 4 * 3 = 12$

$¯ ¯¯¯¯ ¯ C D = ¯ ¯¯¯¯ ¯ E F = \sqrt{{(- 3 - 6)}^{2} + {(7 - 1)}^{2}} = \sqrt{117}$ $bar(CD) = bar(EF) = sqrt((-3-6)^2 + (7-1)^2) = sqrt(117)$

$¯ ¯¯¯¯ ¯ C F = ¯ ¯¯¯¯ ¯ D E = \sqrt{{(- 3 + 5)}^{2} + {(7 - 4)}^{2}} = \sqrt{13}$ $bar(CF) = bar(DE) = sqrt((-3+5)^2 + (7-4)^2) = sqrt(13)$

$Area of Rectangle C D E F = C D \cdot D E = \sqrt{117} \cdot \sqrt{13} = 39$ $"Area of Rectangle " CDEF = CD * DE = sqrt117 * sqrt13 = 39$

$Total Area of the figure A B C D E F = 12 + 39 = 51 sq units$ $"Total Area of the figure " ABCDEF = 12 + 39 = 51 "sq units"$

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This figure is made up of a rectangle and parallelogram. What is the area of this figure? Enter your answer in the box. Do not round any side lengths.

1 Answer

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