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A picture measures are 30cm by 15cm. The mat around the picture is 10 cm wide. Find the area of the mat.
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The correct solution and the correct answer are below :
Assume that the mat is outside the picture. Then the outer dimensions are
30 + 2*10 = 50 cm and 15 + 2*10 = 35 cm.
The total area is:
(30+2*10) cm *(15+2*10) cm = 50*35cm^2 = 1750 cm^2
The area of the picture is:
30 cm * 15 cm = 450 cm^2
The area of the mat alone is (total area - area of picture):
1750 cm^2 - 450 cm^2 = 1300 cm^2
Similar problems were solved, probably, about 100 times in this forum.
The major lesson to learn from the solution is THIS :
the width of the frame must be added TWO TIMES to the measures of a picture to get outer dimensions.
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To see many other similar solved problems, look into the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
- Problems on a circular pool and a walkway around it
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.