Geometry and measurementGrade 6
Area of triangles worksheets
Each problem shows a triangle with its base and height labeled and the height drawn as a dashed line. Students use ½ × base × height. Choose right, height-inside, height-outside or mixed triangles, and whole or half-unit answers.
- Fresh problems every time
- Answer key on its own page
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On this page
The one formula, three looks
The area of any triangle is half of its base times its height. Students find that easy to memorize and harder to apply, because the height is not always a side. In a right triangle it is one of the legs. In an acute triangle it is a line dropped inside the figure. In an obtuse triangle the line falls outside, landing on an extension of the base. This generator shows all three so the formula never gets tied to just one picture.
It is written for sixth grade. Students should already know how to find the area of a rectangle, as practiced on irregular shapes. Afterward, the same ideas support surface area of prisms.
What each problem shows
The base length appears under the bottom edge and the height appears beside a dashed line. The small square marks where the height meets the base at 90°. Slanted sides are never labeled, so there is no tempting extra number to multiply. Bases run from 4 to 18 and heights from 3 to 14, in centimeters, meters, inches, feet, yards or millimeters. Two triangles sit side by side on each row.
The instruction line spells out the formula and notes that the height may fall outside the triangle.
Choosing the settings
- Triangles. "Mixed" gives a blend. "Right triangles" has no dashed line, because a leg is the height. "Height inside" gives acute triangles. "Height outside" gives obtuse triangles, with a second dotted line extending the base. Start with right triangles, then add the other two.
- Allow half-unit answers. On, an odd base times an odd height gives answers such as 31.5. Off, the generator nudges the base so the product is even and every answer is a whole number. Use Off for students not yet comfortable with decimals.
- Number of problems. Four to 12. Eight is the usual page.
Worked example: base 9 cm, height 7 cm
- Name the base and height. Base = 9 cm. Height = 7 cm. Ignore the slanted sides.
- Multiply base by height. 9 × 7 = 63. This is the area of a rectangle that would contain the triangle twice over.
- Take half. 63 ÷ 2 = 31.5.
- Write the unit. 31.5 cm².
A second example for the outside-height type: base 10 in and height 7 in, with the apex sitting beyond the right end of the base. The slanted side is longer than 7 in, but only the height matters. 10 × 7 = 70, half is 35, so the area is 35 in².
Reading the key
- Forgetting the half. The student writes 63. Their answers are exactly double the key.
- Using a slanted side. Not possible on this sheet, since only the base and height are labeled, but a student who measures with a ruler may try it.
- Wrong half on an odd product. 63 ÷ 2 written as 31 or 32 instead of 31.5.
- Wrong unit. Writing cm instead of cm².
Ideas for practice
Cut out a paper rectangle, slice it along a diagonal and show that two matching triangles result. This is the clearest picture of why the area has a half in it. For students who find the dashed height confusing, trace it in a bright color before multiplying. When they are confident, have them hunt down a triangle in a room, measure the base and height, and compute the area.