Question

A rectangular picture frame is 12 inches wide and 18 inches high. This include a 2-inche border (shaded region) around the picture itself. How many square inches are in the border?

Answer 1

Hint : We know that rectangle has a property that the opposite sides of the rectangle are equal and all angle are 90 degree. And also we can say that all sides of a rectangle are perpendicular to each other. And in this question we have to find how many inches in the border that means we have to find the area of the border(shaded region).

Complete answer : Given,
given that:
width of the rectangle ( including border ) = 12 inches
length of the rectancle ( including border ) = 18 inches
and the border width is 2 inches
Now,
Area or border = ( area of outer rectangle ) – ( area of inner rectangle )
For outer rectangle ,
Height (length) = 18 inches
Width (breadth ) = 12 inches
Area of outer rectangle = length × breadth
= (18 × 12) square inches
= 216 square inches
For inner rectangle ,
Height (length) = height of rectangular picture – frame width ( that means border width )
= ( 18 – 2) inches
= 16 inches
Width ( breadth ) = width of rectangular picture – frame width ( Border width )
= ( 12 – 2 ) inches
10 inches
Area of inner rectangle = length × breadth
= (16 × 10) square inches
= 160 square inches
Area or border = ( area of outer rectangle ) – ( area of inner rectangle )
= (216 – 160 ) square inches
=56 square inches

Note : Area of rectangle = length × breadth and
Area of frame = area of outer rectangle – area of inner rectangle.