Grade 8 · Math

8th grade Right triangles in real life and in boxes worksheet

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Right triangles in real life and in boxes

Grade 8 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

To cross the playground, Noah can walk 8 meters along the fence and 11 meters along the wall, or cut straight across. To the nearest tenth of a meter, how much does cutting across save?
Pia's trail map shows a 5-kilometer trail and an 11-kilometer trail meeting at a square corner, plus a straight shortcut. To the nearest tenth of a kilometer, how much shorter is the shortcut?
In the park, Ren could walk 7 meters and then 8 meters around the pond's fenced corner, or take the straight boardwalk. To the nearest tenth of a meter, how much shorter is the boardwalk?
Zee packs a rolled poster in a long box, corner to opposite corner, so it fits snugly. How long is the box's diagonal, in inches?
Ari wraps a gift box and wonders how long a straw would fit, from a bottom corner to the opposite top corner. How long is that diagonal, in inches?
Not to scale. Bo's class uses a big moving box to store art sticks. How long is the box's diagonal, from a bottom corner to the opposite top corner, in inches?
The front of Esme's tent is a triangle with two equal sloping sides of 5 feet and a base 8 feet wide. How tall is the tent at its middle, in feet?
A small house on Jun's street has a roof with two equal sloping sides of 13 feet over a 24-foot-wide base. How tall is the roof at its peak, in feet?
Each slanted leg of Kira's swing set frame is 10 feet long, and the two legs stand 12 feet apart on the ground. How tall is the frame, in feet?
Luz opens a stepladder: each leg is 5 feet long, and the feet stand 6 feet apart on the floor. How tall does the stepladder stand, in feet?

8th grade Right triangles in real life and in boxes worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Right triangles in real life and in boxes. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the right triangle in a story: a ladder on a wall, a kite string, a TV screen, a path across a field.
I can find the missing side, whole or to the nearest tenth, and say which side is the hypotenuse.
I can find how much a shortcut saves, how tall a tent or roof is, and how long a box's diagonal is.

Standard: 8.G.B.7 (real-world, two and three dimensions)

Words to know

right angle: A square corner, like where a wall meets the ground.

hypotenuse: The side across from the right angle; the longest side.

diagonal: A straight line from one corner to the opposite corner.

sketch: A quick drawing of the story's triangle with the right angle marked.

floor diagonal: The line across the bottom of a box, corner to corner.

box diagonal: The line from a bottom corner to the opposite top corner.

Common mistakes

Your child added the lengths of the sides to get the long side. In a right triangle the squares on the short sides add up to the square on the long side; the lengths do not.

Your child found the area of the square on the missing side but gave that area as the length. The length is the number that times itself makes the area.

Your child subtracted one length from another to get a missing short side. The square on the long side minus the square on the known short side gives the missing square. Try a 5-foot rope and a 3-foot gap: 5 − 3 is 2, but the pole is 4 feet.

What to say

Ask: can the shortcut be as long as walking around?

Ask: which number times itself makes it?

Questions parents ask

What is the most common mistake with right triangles in real life and in boxes?

Your child added the lengths of the sides to get the long side. In a right triangle the squares on the short sides add up to the square on the long side; the lengths do not.

How can I help my child with right triangles in real life and in boxes?

Ask: can the shortcut be as long as walking around?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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