Question : A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. The area of the parallelogram is:
Option 1: 42 cm2
Option 2: 60 cm2
Option 3: 84 cm2
Option 4: 96 cm2
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Correct Answer: 84 cm2
Solution : Given: A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. Let ABCD be the parallelogram. The diagonal of a parallelogram divides it into two equal triangles. The half perimeter of one of the triangles, $s$ = $\frac{15+7+20}{2}=21$ cm Area of triangle by heron's formula = $\sqrt{s(s-a)(s-b)(s-c)}$ So, the area of one of the triangles is: = $\sqrt{21(21-15)(21-7)(21-20)}$ = $\sqrt{21×6×14×1}$ = 42 cm2 So, Area of the parallelogram = 2 × Area of one of its triangles = (2 × 42) cm2 = 84 cm2 Hence, the correct answer is 84 cm2.
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Question : The two adjacent sides of a parallelogram are 12 cm and 5 cm respectively. If one of the diagonals is 13 cm long, then what is the area of the parallelogram?
Option 1: 60 cm2
Option 2: 30 cm2
Option 3: 75 cm2
Option 4: 25 cm2
Question : The length of each side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then what is the area of the rhombus?
Option 1: 108 cm2
Option 2: 112 cm2
Option 3: 128 cm2
Question : The ratio of the length of parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 450 cm2, the sum of the length of parallel sides is:
Option 1: 15 cm
Option 2: 36 cm
Option 3: 42 cm
Option 4: 60 cm
Question : The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 450 cm$^2$ the sum of the length of the parallel sides is:
Question : Find the area of the trapezium whose parallel sides measure 14 cm, and 18 cm and the distance between parallel sides is 15 cm.
Option 1: 310 cm2
Option 2: 300 cm2
Option 3: 220 cm2
Option 4: 240 cm2
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