Question

A sheet of cardboard is 1.6 m by 0.8 m. The following shapes are cut from the cardboard: ● a circular piece with radius 12 cm ● a rectangular piece 20 cm by 15 cm ● 2 triangular pieces with base 30 cm and height 10 cm. What is the area of the remaining piece of cardboard in m²? (Consider π = 22/7)

Answer 1

1.17m²

Explanation:

Total area of cardboard=

`1.6 * 0.8 = 1.28m {}^(2)`

Area of circular piece=

`\pi \: r {}^(2) = ( (22)/(7) )(0.12) {}^(2) = (198)/(4375) m {}^(2)`

Area of rectangular piece=

`0.2 * 0.15 = 0.03m {}^(2)`

Area of 2 triangular pieces=

`2( (1)/(2) * 0.3 * 0.1) = 0.03m {}^(2)`

Remaining area of the cardboard= Total area of cardboard - circular piece - 2 triangular pieces

`1.28 - (198)/(4375) - 0.03 -0.03 = (21083)/(17500) =1.17m {}^(2)`