Area, perimeter of trapezium — lesson. Mathematics CBSE, Class 8.

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Area of trapezium: To obtain the area of a trapezium, multiply the sum of the bases by the height and then divide by \(2\).

The area of a trapezium is computed with the following formula:

Area of trapezium \(=\)

\frac{1}{2} \times (a + b) \times (h)

square units.

(where \(a\) and \(b\) is bases (parallel sides) and \(h\) is leg or height (between the non-parallel sides)).

Area of the trapezium \(ABCD\):

Proof: Area of a trapezium \(ABCD\).

Area of trapezium \(ABCD\) \(=\)

\frac{1}{2} (AB + DC) \times (h)

\(square units\).

\(=\) area of triangle

(DEA)

\(+\) area of rectangle

(DEFC)

\(+\) area of triangle

(CFB)

\(=\)

\frac{1}{2} \times AE \times DE

\(+\)

DE \times EF

\(+\)

\frac{1}{2} \times FB \times CF

\(=\)

\frac{1}{2} \times AE \times h

\(+\)

h \times EF

\(+\)

\frac{1}{2} \times FB \times h

\(=\)

\frac{1}{2} \times (AE + 2 EF + FB) \times h

\(=\)

\frac{1}{2} \times (AE + EF + CD + FB) \times h

\(=\)

\frac{1}{2} \times (AE + EF + FB + CD) \times h

\(=\)

\frac{1}{2} \times (AB + CD) \times (h)

\(=\)

\frac{1}{2} \times (a + b) \times (h)

\(=\) \(\frac{1}{2}\times\)(\(\text{sum of parallel side}\)) \(\times\)\((\text{height})\) square units.

Therefore, Area of trapezium \(ABCD =\)

\frac{1}{2} \times (a + b) \times (h)

Perimeter of trapezium: The Perimeter is the sum of all side lengths.

The perimeter of a trapezium is computed with the following formula:

Perimeter of trapezium \(=\) \(a + b + c + d\) (where \(a\), \(b\) are denoted as bases (parallel sides) and \(c\), \(d\) are denoted as legs (non-parallel sides)).

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2. Area, perimeter of trapezium

Theory: