Area, Perimeter & Composite Shapes
Calculating perimeter and area of rectangles, squares, parallelograms, trapezoids, and composite/irregular shapes — excludes circles (see circles) and triangles (see triangles)
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Imagine you are building a top-secret, zombie-proof fort in your backyard! 🧟♂️ To keep the zombies out, you need to build a strong fence all the way around it. The total length of that fence is the perimeter. It is simply the distance around the outside edge of a shape. You find it by adding up all the outside lines. Easy, right?
Now, imagine you want to cover the floor of your awesome new fort with super-soft, lava-proof carpet. 🌋 The amount of carpet you need to cover the entire floor is the area. Area measures the flat space inside a shape. For a basic rectangle, you just multiply the length by the width. Think of perimeter as the crust of a pizza, and area as all the delicious cheese and pepperoni in the middle! 🍕
On the SSAT, the test makers love to test these concepts, but they might try to trick you by combining shapes or cutting pieces out of them. Don't panic! If they cut a piece out of a rectangle, just trace the new outside edges with your pencil to figure out the new perimeter. If they smash two shapes together to make a weird blob, just break it apart! Find the area of each normal shape, and then add them up. With a little practice, you will be a measurement master!
Practice Questions
4 practice questions for SSAT Middle Level
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- First, find the total area of the rectangular floor by multiplying the length by the width: square feet. Next, find the area of the square rug by squaring its side length: square feet. To find the area of the floor not covered by the rug, subtract the rug's area from the floor's total area: square feet.
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- First, calculate the total area of the rectangle: . Next, calculate the area of the triangle. The base of the triangle is 20 and its height is 10 (since it stretches from the bottom edge to the top edge of the rectangle). The area of the triangle is . Finally, subtract the area of the triangle from the total area of the rectangle to find the area outside the triangle: .
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- To find the total area, calculate the area of the square and the right triangle separately. The area of the square is square centimeters. The right triangle has a height of 8 centimeters (since it shares a side with the square) and a base of 6 centimeters. The area of the triangle is square centimeters. The total area of the composite figure is square centimeters.
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- First, find the side length of one square. Since the area is 49 square inches, the side length is inches. When two such squares are placed side-by-side, they form a rectangle with a width of 7 inches and a length of inches. The perimeter of a rectangle is . Therefore, the perimeter is inches.
Tips & Strategies
- Draw it out! The SSAT loves to give you word problems without pictures. Sketching the shape and labeling the sides prevents silly mistakes.
- Watch out for the 'add to both sides' trick. If a border goes around a whole garden, it adds to the left AND right sides, so you have to double the border width!
- Trace the perimeter with your pencil. When finding the perimeter of a weird, mashed-up shape, physically tracing the outside lines helps you make sure you didn't miss any sides.
Common Mistakes
- Watch out for mixing up the formulas! A classic mistake is multiplying when you should add (finding area instead of perimeter) or adding when you should multiply.
- Don't forget the hidden sides! When two shapes are stuck together (like a triangle on top of a square), the line where they touch is inside the new shape, so it does NOT count towards the perimeter.
Frequently Asked Questions
Do I need to memorize area formulas for the SSAT?
Yes! The SSAT expects you to know the area of squares, rectangles, triangles (Area = ), and circles. Memorize these early!
What if a shape is super weird and I don't know the formula?
Break it into smaller, normal shapes! A weird L-shape is really just two rectangles glued together. Find the area of each piece and add them up.
Why do we use 'square units' for area?
Because you are literally counting how many little squares fit inside a shape! Perimeter is just a line (like a piece of string), so it uses regular units like inches.