Answer :

(i) Since all the three sides of a triangle are given as equal it forms a equilateral triangle with sides measure = 10 cm


Area of a equilateral triangle


= where a is the side of the triangle


Here, Area of equilateral triangle =


=


= 25 √3 cm2


(ii) In the triangle two sides AB and AC (both a) are equal and


The base BC (b) = 8 cm


Area of the isosceles triangle with the given equal length sides and base =


=


= 4× √84


= 4× 9.17


= 36.66cm2


(iii) In the given trapezium ABCD, AD BC and DC is transversal (both are at 90°)


Area of trapezium


= 1/2 × sum of the parallel two sides of a trapezium


× the distance between the parallel sides


Here, parallel sides AD= 5cm and BC = 4 cm and distance between them, DC= 3cm


Area of trapezium = 1/2 × (5+4) × 3


= 1/2 × 9 × 3


= 13.5cm2


(iv) Given in the trapezium ABCD parallel sides are DC and AB and distance between parallel sides AD = 9 cm ( arrow means parallel sides)


AD= 9 cm


DC= 40 cm


AB = 15cm


And ADC= 90°


Area of trapezium


= 1/2 × sum of the parallel two sides of a trapezium


× the distance between the parallel sides


= 1/2 × (15 +40) × 9


= 1/2 × 55 × 9


= 247.5 cm2


(v) Arrows in the figure indicates side DC = AB and AD = BC hence it is a rectangle with both the pair of opposite sides parallel and angle between adjacent sides is 90°


DC = AB = 38


ADC = 90° (given)


AC = 42cm


In Δ ADC


AC= 42


DC = 38


ADC = 90


By using the Pythagoras theorem


AC2 = AD2 +DC2


422 = AD2 + 382


1764 – 1444 = AD2


AD = √320


AD = 17.89cm


Area of rectangle = l × b, where l and b are length and breadth of rectangle


Area of rectangle ABCD = 17.89 × 38


= 679.76cm2


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