Question

What is a trapezoid?

Answer 1

Hint: This type of question depends on the quadrilateral and types of quadrilateral along with the properties. A quadrilateral is a closed shape made up of four vertices and four sides. A quadrilateral is a 2D figure whose interior angle sum is \[{{360}^{\circ }}\] that means if we add all the internal angles then the sum is equal to \[{{360}^{\circ }}\].

Complete step by step solution:
A trapezoid is a type of quadrilateral having only one pair of parallel sides. The parallel sides are known as ‘bases’ and the other two sides are called ‘legs’ or lateral sides. The perpendicular distance between the parallel sides is known as ‘altitude’.

Now, here we are considering trapezoid ABCD, the sides AB and CD are parallel sides. The line segment BE is the altitude of the trapezoid.
As we know that, the trapezoid is a four sided two dimensional figure same as that of square, rectangle, and parallelogram. Hence, it also has its perimeter and area. So that we can write the formula for perimeter and area of a trapezoid are as follows:
Area – we can calculate the area of a trapezoid by taking the average of parallel sides (two bases) and multiplying it with the altitude.
\[\Rightarrow \text{Area = }\dfrac{1}{2}\times (a+b)\times h\]
Perimeter – The perimeter of a trapezoid is the sum of all its sides. Hence, if a trapezoid is with sides a, b, c and d then the perimeter is given by,
\[\Rightarrow \text{Perimeter = }a+b+c+d\]

Note: While solving this problem students may make mistakes in trapezoid and parallelogram. Also when students write formulae for areas of the trapezoid they have to take care about the altitude of the trapezoid which is perpendicular distance between the parallel sides and not equal to either of the non-parallel sides.