Question

Here Is a trapozhum and a squnro, The lengths of the parnllel sides of the

trapezhum are 10 cm and 14 cm, The helght of tho trhpoziurm is 12 cm. The nren of
the squpre is equal to the aren of the trapeziurn. Work out the perimeter of the
square

Answer 1

48 cm

Explanation:

Here Is a trapezium and a square, The lengths of the parallel sides of the trapezium are 10 cm and 14 cm, The height of the trapezium is 12 cm. The area of the square is equal to the area of the trapezium. Work out the perimeter of the square.

Solution:

The area of the trapezium is given by:

A = (1/2)(a + b)h

where h is the height of the trapezium = 12 cm, a and b are the parallel sides. Given that a = 10 cm, b = 14 cm, hence:

A = (1/2)(10 + 14)12 = 144 cm²

Area of trapezium = Area of square

Area of square = 144 cm²

Area of square = length * length = length²

length² = 144 cm²

length = √144 = 12 cm

Perimeter = 4 * length = 4 * 12 cm = 48 cm