Question

Area and perimeter


9=


10=

Answer 1

9). 15 miles

10). 12880.8 in²

Explanation:

9). Total distance to be covered by Kelly = Perimeter of the given triangle

= Sum of three sides of the triangle

To know the length of Laurel drive (Hypotenuse of the triangle), we will apply Pythagoras theorem in the given triangle,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

= (2.5)²+ 6²

= 6.25 + 36

Hypotenuse =
`√(42.25)`

= 6.5 mi.

Therefore, total distance covered by Kelly = 6.5 + 2.5 + 6

= 15 mi.

10). Amount of paper required to cover one desk of the class

= Area of the trapezoid shown in the figure

=
`(1)/(2)(b_1+b_2)h`

Here,
`b_1` and
`b_2` are the parallel sides of the trapezoid

And 'h' is the distance between the parallel sides.

By applying Pythagoras theorem in ΔPRT,

PR² = RT² + PT²

PT =
`√(PR^2-RT^2)`

PT =
`√((18)^2-2^2)`

=
`√(324-4)`

=
`√(320)`

= 17.89 in.

Area of the trapezoid PQRS =
`(1)/(2)(PQ+RS)(PT)`

=
`(1)/(2)(22+26)(17.89)`

= 429.36 in²

Therefore, paper required to cover 30 desks = 30 × 429.36

= 12880.8 in²