ISEE Lower Level Mathematics Achievement Quiz
Practice Perimeter From Diagrams in ISEE Lower Level Mathematics Achievement with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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A large rectangle is 20 feet long and 10 feet wide. A smaller rectangular porch that is 6 feet long and 4 feet wide juts out from the middle of one of the 20-foot sides. What is the perimeter of the combined shape of the house and porch?
This quiz focuses on Perimeter From Diagrams, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
A large rectangle is 20 feet long and 10 feet wide. A smaller rectangular porch that is 6 feet long and 4 feet wide juts out from the middle of one of the 20-foot sides. What is the perimeter of the combined shape of the house and porch?
Explanation: Start with the perimeter of the large rectangle: 2 * (20 + 10) = 60 feet. When the porch is added, a 6-foot section of the house's wall is replaced by the three outer walls of the porch. The lengths of these three walls are 4 feet, 6 feet, and 4 feet. The change to the perimeter is -6 (the removed wall section) + 4 + 6 + 4 = +8 feet. The new total perimeter is 60 + 8 = 68 feet.
A rectangular poster has a width of 10 inches. Its length is 4 inches greater than its width. What is the perimeter of the poster?
Explanation: First, determine the length of the poster. The width is 10 inches, and the length is 4 inches greater, so the length is 10 + 4 = 14 inches. The perimeter of a rectangle is P = 2 × (length + width). So, P = 2 × (14 + 10) = 2 × 24 = 48 inches.
A rectangular backyard is 25 feet long and 18 feet wide. The entire yard is enclosed by a fence, but there is a 3-foot wide gate in the fence. How many feet of fencing material were used, not including the gate?
Explanation: First, calculate the total perimeter of the backyard: P = 2 × (25 + 18) = 2 × 43 = 86 feet. The gate is part of this perimeter, but it is not made of fencing material. So, subtract the width of the gate from the total perimeter: 86 feet - 3 feet = 83 feet. Therefore, 83 feet of fencing material were used.
A triangle has a perimeter of 30 feet. The second side is 2 feet longer than the first side. The third side is 4 feet longer than the first side. What is the length of the shortest side?
Explanation: Let the shortest side be 'x'. The other sides are 'x + 2' and 'x + 4'. The perimeter is the sum of the sides: x + (x + 2) + (x + 4) = 30. This simplifies to 3x + 6 = 30. Subtract 6 from both sides: 3x = 24. Divide by 3: x = 8. The shortest side is 8 feet.
A square has a side length of 8 cm. A rectangle has a length of 10 cm and a width of 5 cm. What is the difference between the perimeter of the square and the perimeter of the rectangle?
Explanation: First, find the perimeter of the square: P_square = 4 × 8 cm = 32 cm. Next, find the perimeter of the rectangle: P_rectangle = 2 × (10 cm + 5 cm) = 2 × 15 cm = 30 cm. The difference is 32 cm - 30 cm = 2 cm.
A shape is made by joining three identical squares in a row, side to side. If the side of each square is 4 centimeters, what is the perimeter of the entire shape?
Explanation: The shape is a long rectangle composed of three squares. The top side has a length of 4+4+4=12 cm. The bottom side also has a length of 12 cm. The left and right sides each have a length of 4 cm. The perimeter is the sum of the outside edges: 12 + 12 + 4 + 4 = 32 cm. Alternatively, there are 8 exterior sides of length 4 cm, so 8 x 4 = 32 cm.
A square garden has a side length of 15 feet. A brick path that is 3 feet wide is built around the entire outside of the garden. What is the perimeter of the outer edge of the brick path?
Explanation: The garden is a 15-foot square. The 3-foot path adds 3 feet to the top, bottom, left, and right. The new, larger square (garden plus path) has a side length of 15 + 3 + 3 = 21 feet. The perimeter of this new square is 4 × 21 = 84 feet.
A rectangular field has a length of 30 meters and a width of 20 meters. A farmer walks around the entire edge of the field one time. What is the total distance the farmer walks?
Explanation: The distance around the edge of a field is its perimeter. The formula for the perimeter of a rectangle is P = 2 × (length + width). In this case, P = 2 × (30 meters + 20 meters) = 2 × (50 meters) = 100 meters. The farmer walks 100 meters.
A rectangular photograph is 7 inches wide and 9 inches tall. It is placed in a frame that adds a border of 2 inches to every side. What is the perimeter of the outside edge of the framed photograph?
Explanation: The frame adds 2 inches to each side. The new width is 7 + 2 + 2 = 11 inches. The new height is 9 + 2 + 2 = 13 inches. The perimeter of the outside of the frame is P = 2 × (11 + 13) = 2 × 24 = 48 inches.
An L-shaped room has six walls. The outside wall measurements are 12 feet, 15 feet, 7 feet, 6 feet, 5 feet, and 9 feet. What is the perimeter of the room?
Explanation: The perimeter of a shape is the sum of the lengths of all its sides. To find the perimeter of the L-shaped room, add all the given wall measurements: 12 + 15 + 7 + 6 + 5 + 9 = 54 feet.
An isosceles triangle has a perimeter of 40 inches. The shortest side, which is the base, measures 10 inches. What is the length of one of the two equal sides?
Explanation: The perimeter is the sum of the three sides. Let the length of one of the equal sides be 's'. The perimeter is s + s + 10 = 40 inches. Combining the 's' terms gives 2s + 10 = 40. Subtract 10 from both sides: 2s = 30. Divide by 2 to find s: s = 15 inches.
A rectangle has a perimeter of 50 feet. Its length is 15 feet. What is its width?
Explanation: The perimeter of a rectangle is P = 2 × length + 2 × width. We know P=50 and length=15. So, 50 = 2 × 15 + 2 × width. This simplifies to 50 = 30 + 2 × width. Subtract 30 from both sides: 20 = 2 × width. Divide by 2 to find the width: width = 10 feet.
The perimeter of a square painting is 48 inches. What is the length of one side of the painting?
Explanation: A square has four equal sides. The perimeter is the sum of the lengths of all four sides, so P = 4 × side. To find the length of one side, divide the perimeter by 4. Side = 48 inches / 4 = 12 inches.
A rectangular flower bed that is 12 meters long and 5 meters wide is built against a long brick wall. Fencing is put around the other three sides of the flower bed. What is the total length of the fencing used?
Explanation: The fencing is needed for two sides of 5 meters and one side of 12 meters. The side against the wall does not need fencing. The total length of fencing is 5 meters + 12 meters + 5 meters = 22 meters.
A triangular garden has sides measuring 2 feet, 30 inches, and 3 feet. What is the perimeter of the garden in inches? (1 foot = 12 inches)
Explanation: To find the perimeter in inches, first convert all measurements to inches. The first side is 2 feet × 12 inches/foot = 24 inches. The second side is 30 inches. The third side is 3 feet × 12 inches/foot = 36 inches. Now, add the lengths of the three sides: 24 + 30 + 36 = 90 inches.
Two identical squares, each with a side length of 5 cm, are placed side-by-side to form a single, larger rectangle. What is the perimeter of this new rectangle?
Explanation: When two 5 cm squares are placed side-by-side, they form a rectangle with a length of 5 + 5 = 10 cm and a width of 5 cm. The perimeter of this new rectangle is P = 2 × (10 + 5) = 2 × 15 = 30 cm.
The perimeter of an equilateral triangle is 27 centimeters. What is the length of one of its sides?
Explanation: An equilateral triangle has three sides of equal length. To find the length of one side, divide the total perimeter by 3. Side length = 27 cm / 3 = 9 cm.
A figure in the shape of a plus sign is made from five identical squares, each with a side length of 3 inches. What is the perimeter of the plus-sign shape?
Explanation: The plus-sign shape has 12 sides on its exterior. Each of these sides is a side of one of the squares, so each has a length of 3 inches. The total perimeter is the number of exterior sides multiplied by the length of a side: 12 × 3 inches = 36 inches.
A large rectangular piece of paper is 10 inches by 8 inches. A small square with a side length of 3 inches is cut out from one of the corners. What is the perimeter of the new shape?
Explanation: The perimeter of the original rectangle is 2 × (10 + 8) = 36 inches. When a square is cut from a corner, two sides of the rectangle are shortened by 3 inches each, but two new sides of 3 inches each are created. The change in perimeter is -3 -3 + 3 + 3 = 0. Therefore, the perimeter of the new shape is the same as the original rectangle, 36 inches.
A regular hexagon has six equal sides. If one side of a regular hexagon measures 8 meters, what is its perimeter?
Explanation: A regular hexagon has 6 equal sides. The perimeter is the total length around the shape. To find the perimeter, multiply the length of one side by the number of sides: 8 meters/side × 6 sides = 48 meters.