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

Answer:

Square inches of fabric required = 12

Step-by-step explanation:

Distance from (a,b) to (c,d) $=\sqrt{(c-a)^2+(d-b)^2}$.

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

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

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

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$, where $s=\frac{a+b+c}{2}$

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

$s=\frac{5+3+4}{2}=6$

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

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

Square inches of fabric required = 12