Question

if h is height a and b are length of parallel sides of the trapezium when area of trapezium is given by​

Answer 1

Area of trapezium ABCD = Area of ∆ ABD + Area of ∆ CBD

= 1/2 × a × h + 1/2 × b × h

= 1/2 × h × (a + b)

= 1/2 (sum of parallel sides) × (perpendicular distance between them)

Answer 2

Answer:

The area of the trapezium is given by  $\frac{1}{2}$ (a+b) × h

Step-by-step explanation:

Given:

a and b are the parallel sides of the trapezium

h is the distance between the parallel sides

To find: Formula for the area of the trapezium.

Solution:

Trapezium:

• A quadrilateral with one set of parallel opposite sides is a trapezium.
• The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively.
• The parallelogram is occasionally referred to as a trapezoid with parallel sides.

Properties of trapezium:

• The trapezium's four angles add up to 360° in total. 
• Two of the sides of a trapezium are parallel, and the other two are not.
• Regular trapezium diagonals cut each other in half.

Given a and b are the length of the parallel sides of the trapezium

h is the height of the trapezium

Area of the trapezium  ABCD = Area of Δ ABD + Area of ΔCBD

     = $\frac{1}{2}$ × a × h + $\frac{1}{2}$ × a × h

     =  $\frac{1}{2}$ × h (a+ b)

       =  $\frac{1}{2}$  (sum of parallel sides) × (perpendicular distance between them.

      =  $\frac{1}{2}$ (a+b) × h

Final answer:

The area of the trapezium is given by $\frac{1}{2}$ (a+b) × h

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