A picture 15 inch x 30 inch is surrounded by a mat 2 inch wide.The aea of the mat in swuare inches is

a. 60
b. 94
c. 124
d. 128
e. 196

I know the answer is e, but i don't know how to do it, anyone can tell me how to do it, thank you

19 * 34 = 646

15 * 30 = 450

646 - 450 = 196 square inches

I don't understant,why 15 inch x 30 inch is surrouded by a mat 2 inch wide. 15+2 x 30+2 = 17 x 32

why + 4 ?

15+4 x 30+4

19 X 34 ?

oh , because two side right

YES.

To find the area of the mat surrounding the picture, we need to calculate the difference in area between the outer rectangle (including the mat) and the inner rectangle (just the picture).

First, let's find the area of the outer rectangle, which is formed by adding 2 inches of width to each side of the picture. The length of the outer rectangle will be the sum of the original length plus twice the mat width, and the width of the outer rectangle will be the sum of the original width plus twice the mat width.

Given:
Picture length = 15 inches
Picture width = 30 inches
Mat width = 2 inches

Length of outer rectangle = Picture length + (2 * Mat width)
= 15 inches + (2 * 2 inches)
= 15 inches + 4 inches
= 19 inches

Width of outer rectangle = Picture width + (2 * Mat width)
= 30 inches + (2 * 2 inches)
= 30 inches + 4 inches
= 34 inches

Next, let's calculate the area of the inner rectangle formed by just the picture.

Area of the inner rectangle = Picture length * Picture width
= 15 inches * 30 inches
= 450 square inches

Now, subtract the area of the inner rectangle from the area of the outer rectangle to find the area of the mat:

Area of the mat = Area of the outer rectangle - Area of the inner rectangle
= (Length of outer rectangle * Width of outer rectangle) - Area of the inner rectangle
= (19 inches * 34 inches) - 450 square inches
= 646 square inches - 450 square inches
= 196 square inches

Therefore, the area of the mat in square inches is 196 square inches. Hence, the correct answer is (e) 196.