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11.
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?

The diagonal BD of quadrilateral ABCD is joined and it divides the quadrilateral into two triangles.
Now,
Area of quadrilateral ABCD = Area of

straight capital delta space ABD

+ Area of

space space increment space BCD

open parentheses 1 half straight b cross times straight h close parentheses space plus space open parentheses 1 half straight b cross times straight h close parentheses

2 space open parentheses 1 half straight b space cross times space straight h close parentheses space equals space bh

Infact ABCD is a parallelogram.
∴ Area of a parallelogram ABCD = h x h
Area of a parallelogram = Base x Height
We know that a parallelogram can also be a trapezium. We already know that
Area of trapezium ABCD =

1 half

(Sum of parallel sides)
x [Perpendicular distance between the parallel sides]
=

space space 1 half cross times left parenthesis straight b plus straight b right parenthesis space straight x space straight h

space 1 half cross times left parenthesis 2 straight b right parenthesis cross times straight h space equals space bh

or Area of parallelogram ABCD = bh.
Yes, the above relation agrees with formula that we know already.

The diagonal BD of quadrilateral ABCD is joined and it divides the qu

The diagonal BD of quadrilateral ABCD is joined and it divides the qu

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Short Answer Type

12.

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

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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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