Area and Perimeter

Area and Perimeter

Try some of the examples below and if you need any help, just look at the solution I have written. Cheers ! =) .
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EXAMPLE:

$${\small 1.\enspace}$$ In the figure below, ABC is an isosceles triangle, $${\small \angle {A} = 90^{\large{\circ}}}$$ and PQRS is a square of side 1 cm. Find the area of $${\small \triangle ABC}$$.
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$${\small 2.\enspace}$$ In the figure below, ABEG is a rectangle with E and G are the centres of the circles. If BE $$=$$ 7 cm and the areas of the green regions ABC and CDF are equal, find GE.
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$${\small 3.\enspace}$$ If rectangle ABCD is three times as large as $${\small \triangle CDX}$$ and four times as large as $${\small \triangle BCY}$$, what fraction of the rectangle is coloured orange?
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$${\small 4.\enspace}$$ In the figure below, ABCD is a parallelogram. M and N are the midpoints of AD and BC respectively.
$${\small\hspace{1.2em}\left(a\right).\hspace{0.8em}}$$ What fraction of the parallelogram is the pink area?
$${\small\hspace{1.2em}\left(b\right).\hspace{0.8em}}$$ If the pink area is a rectangle, find the ratio of AB : BC.
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$${\small 5.\enspace}$$ ABCD is a rhombus. E and F are the midpoints of AD and CD respectively. What fraction of the rhombus is coloured yellow?
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$${\small 6.\enspace}$$ OAB is a quadrant of radius 7 cm. OCA and OCB are semicircles. Find the total area of the red region.
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$${\small 7.\enspace}$$ Given that AB : BC $$=$$ EF : FG $$=$$ 1 : 2, CD : DE $$=$$ 2 : 3 and ACEG is a rectangle, find the ratio of the areas of parts P, Q, R and S.
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$${\small 8.\enspace}$$ The shape shown below is bounded by the arc of a three-quarter circle of radius 1 cm and the arcs of two quadrants with radii 2 cm and 3 cm. Find the area of the shape.
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