In the given figure (not drawn to scale), ABCD and WXYZ both are rhombus, 2 semi- circles and 2 identical triangles are drawn on the sides of rhombus WXYZ. Which of the following options is correct ?

Options

A. Area of `Delta WPZ ` is 104 `cm^(2)`
B. Circumference of the semi - circle is 20 cm
C. Area of rhombus ABCD is 24 ` cm^(2)`
D. None of these

Answer

C

Explanation

In the given figure , we have
Area of rhombus `ABCD = (1)/(2) xx AC xx BD = (1)/(2) xx 6 xx 8 `
`= 24 cm^(2)`
In ` Delta XOY, angle XOY = 90^(@)`
`:. XY^(2) = OX^(2) + OY^(2)" "` (By Pythagoras theorem )
`rArr XY^(2) = 8^(2) + 15 ^(2) = 289`
`rArr XY = 17 cm`
So, WZ = 17 cm = XW = YZ
`:.` Area of `Delta WPZ = (1)/(2) xx WZ xx 8 = (1)/(2) xx 17 xx 8 = 68 cm^(2)`
Also, circumference of semi-circle = `pi r + 2 r`
` = (22)/(7) xx (17)/(2) + 2 xx (17)/(2) = 43 . 71 ` cm