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We know that parallelogram is also a quadrilateral. Let us also split such a quadrilateral into two triangles, find their areas and hence that of the parllelogram. Does this agree with the formula that you know already?

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Short Answer Type

12.
Find the area the quadrilateral LMNOP (as shown in the figure).

Diagonal LN = 8 cm
Perpendicular MX = 4.5 cm
Perpendicular OY = 3.5 cm
∵ Sum of the perpendiculars = MX + OY = 4.5 cm + 3.5 cm = 8 cm
∴ Area of the quadrilateral = $1 half cross times$ (A diagonal ) x (Sum of the lengths of the perpendiculars on it from opposite vertices)
$equals 1 half cross times space 8 space cross times space 8 space cm squared space equals space 32 space cm squared$

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13. A parallelogram is divided into two congruent triangles by drawing a diagonal across it. Can we divide a trapezium into two congruent triangles?

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14. Find the area of a rhombus whose diagonals are 12 cm and 9.2 cm.

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Long Answer Type

15. Find the area of these quadrilaterals:

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16. Divide the following polygons into parts (triangles and trapezium) to find out its area.

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17.

Polygon ABCDE is divided into parts as shown below. Find its area of AD = 8 cm, AH = 6 cm, AG = 4 cm, AF = 3 cm and perpendiculars BF = 2 cm, CH = 3 cm, EG = 2.5 cm.

Area of polygon ABCDE = Area of $straight capital delta space AFB$ + .........

Area of $increment space AFB$ = $1 half cross times AF cross times BF space equals space 1 half cross times 3 cross times 2 space equals space..........$

Area of trapezium FBCH = $FH cross times fraction numerator left parenthesis BF plus CH right parenthesis over denominator 2 end fraction$

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Area of $increment space CHD space equals space$ $1 half cross times HD cross times CH space equals space........$

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So, the area of polygon ABCDE = ........

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18.

Find the area of polygon MNOPQR if MP = 9 cm, MD = 7 cm, MC = 6 cm, MB = 4 cm, MA = 2cm. NA, QC, QD and RB are perpendiculars to diagonal MP.

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Short Answer Type

19.

The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

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20. The area of a trapezium is 34 cm² and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.

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