Question

A seamstress is making a decorative pillow and wants to cover both sides of the pillow with special fabric. The pillow is in the shape of a triangle with vertices (7, 7) (10, 3) (7, 3). How many square inches of fabric will she need if each unit on the grid is one inch?

Answer 1

The seamstress will need 12 inches of special fabric. 

Answer 2

Square inches of fabric required = 12

Explanation:

Distance from (a,b) to (c,d)
`=√((c-a)^2+(d-b)^2)`.

Distance from (7, 7) to (10, 3)
`=√((10-7)^2+(3-7)^2)=5\texttt{ inch}`

Distance from (10, 3) to (7, 3)
`=√((7-10)^2+(3-3)^2)=3\texttt{ inch}`

Distance from (7, 3) to (7, 7)
`=√((7-7)^2+(7-3)^2)=4\texttt{ inch}`

Area of triangle
`=√(s(s-a)(s-b)(s-c))`, where
`s=(a+b+c)/(2)`

Here a = 5, b = 3 and c = 4

`s=(5+3+4)/(2)=6`

Area of triangle
`=√(6(6-5)(6-3)(6-4))=12\texttt{ square inch}`

Area of pillow = 2 x Area of triangle = 2 x 6 = 12 square inch

Square inches of fabric required = 12