Let us write by calculating the area following regions.

(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