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51.

In the given figure, ABCD is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If `AD = sqrt25` cm then area of the rectangle is A. `32 cm^(2)`B. `40 cm^(2)`C. `44 cm^(2)`D. `48 cm^(2)`

Answer» Correct Answer - B
`AB^(2)=AC^(2)-BC^(2)=(AC^(2)-AD^(2))={(10^(2))-2(sqrt5)^(2)}=(100-20)=80`
`rArr AB=sqrt80 = sqrt(16xx5) = 4sqrt5 cm`.
`therefore ar("rect. ABCD")=(ABxxAD)=(4sqrt5xx2sqrt5)cm^(2) = 40 cm^(2)`
Discussion
52.

Look at the statement given below: I. A parellelogram and a rectangle on the same base and between the same parallels are equal in area. II. In a ||gm ABCD, it is given that AB = 10 cm. The altitudes DE and AB and BF on AD being 6 cm and 8 cm respectively, then AD = 7.5 cm. III. Area of a ||gm `=(1)/(2)xx "base" xx "altitude."` Which is true? A. I onlyB. II onlyC. I and IID. II and III

Answer» Correct Answer - C
Clearly I is true.
`ABxxDE =(10xx6)and(ADxxBF)=(7.5xx8)=60`
`therefore` II is true.
But, III is clear false,as we know that
area of a ||gm = base `xx` altitude.
Discussion
53.

In the given figure, ABCD is a trapezium in which AB||DC such that AB = a cm and DC = b cm. If E and F are the midpoints of AB and BC respectively then ar(ABFE) : ar(EFCD) = ? A. `a : b`B. `(a+3b): (3a+b)`C. `(3a+b) : (a+3b)`D. `(2a + b) : (3a + b)`

Answer» Correct Answer - C
Discussion
54.

If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram isA. `1 : 3`B. `1 : 2`C. `3 :1`D. `1 : 4`

Answer» Correct Answer - B
We know that, if a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.
i.e., Area of triangle `= (1)/(2)` Area of parallelogram
`rArr" "` `("Area of triangle")/("Area of parallelogram") = (1)/(2)`
`therefore" "` `"Area of triangle " : " Area of parallelogram " = 1 : 2`
Discussion