4-9 More Area Problems Name______
Date______
Solve each Problem. Don’t forget to include the units in your answer.
1. A rectangle is 6 cm longer than it is wide. If the length and the width are both increased by 3 cm, the area is increased by 99 cm2. Find the original dimensions.
2. A tinsmith has two pieces of sheet metal with the same area. One is a square and the other is a rectangle 18 cm longer than the square but 9 cm less wide than the square. Find the total are of each piece of metal.
3. A rectangle garden is 10 m longer than it is wide. The owner wants to increase the size of the garden. If he adds an additional 3 m to each of the four sides, he will gain an additional 216 m2 of garden area. What are the dimensions of the garden?
4. A painting is 3 inches longer than it is wide. It is set in a frame 2 inches wide on each side. If the area of the frame is 100 in2, what are the dimensions of the painting?
5. A mason builds two patios with the same area. One is a square and the other is a rectangle 10 m longer than the square but 8 m less wide than the square. What is the area of each patio?
6. A rectangle is twice as long as it is wide. If both its dimensions are increased by 4 m, its area is increased by 88 m2. Find the original dimensions.
7. A poster is 25 cm taller than it is wide. It is mounted on a piece of cardboard so that there is a 5 cm border on all sides. If the area of the border alone is 1350 cm2, what are the dimensions of the poster?
8. A brick patio is twice as long as it is wide. It is bordered on all sides by a garden 1.5 m wide. Find the dimensions of the patio if the area of the garden is 54 m2.
9. A house has two rooms of equal area. One room is square and the other room is rectangle 4 ft narrower and 5 ft longer than the square one. Find the area of each room.