Question

A square sheet of paper has a side of 10 cm. A triangular piece is removed from one of its corners as shown. Find the area of the remaining part of the paper sheet.

Answer 1

Hint: Find the dimensions of the triangular piece using the properties of the square and subtract the area of it from the total area of the square to get the required answer.

Complete step-by-step answer:

Observing the triangular piece of the sheet of paper and thus getting the altitude = ( 10 – 6 )cm = 4 cm and the base ( 10 – 8 )cm = 2cm of the triangle .

Area of the original square sheet = ${10^2} = 100c{m^2}$ ( area of the square = $sid{e^2}$ )

Area of triangular piece = $\dfrac{1}{2} \times 2 \times 4 = 4c{m^2}$

Thus the area of the remaining part of the sheet = $\left( {100 - 4} \right)c{m^2} = 96c{m^2}$

Note: Remember that the altitude and the base of the triangle can be interchanged in this question as it forms a right triangle. Observe the dimensions carefully and recall the formula of area of the triangle and square in such types of questions.