The area of a triangle is the amount of space contained within the triangle. It is usually measured in square units, such as square centimeters or square inches. To find the area of a triangle, you can use the following formula:

Area = (base * height) / 2

where base is the length of one of the sides of the triangle, and height is the distance from the base to the opposite vertex.

The perimeter of a triangle is the total length of all the sides of the triangle. To find the perimeter of a triangle, you simply add up the lengths of all the sides.

For example, consider the triangle shown below:

[asy] unitsize(1 cm); draw((0,0)–(4,0)–(2,3)–cycle); label(“\$a\$”, (0,0)–(4,0), S); label(“\$b\$”, (4,0)–(2,3), NE); label(“\$c\$”, (2,3)–(0,0), NW); label(“\$A\$”, (2,1.5), N); label(“\$B\$”, (4,0), S); label(“\$C\$”, (0,0), S); [/asy]

In this triangle, the base is the side with length 4 cm, and the height is the distance from vertex A to the base, which is 3 cm. Therefore, the area of this triangle is (4 * 3) / 2 = 6 cm^2. The perimeter of this triangle is the sum of the lengths of all the sides, which is 4 + 3 + 5 = 12 cm.

I hope this helps! Let me know if you have any other questions.

### Sample Test Questions

1. A triangle has a base of 6 cm and a height of 8 cm. What is the area of the triangle?
2. A triangle has sides of lengths 7 cm, 9 cm, and 11 cm. What is the perimeter of the triangle?
3. A triangle has an area of 30 cm^2 and a base of 10 cm. What is the height of the triangle?
4. A triangle has a perimeter of 20 cm and sides of lengths 4 cm, 7 cm, and 9 cm. What is the area of the triangle?
5. A triangle has a height of 12 cm and an area of 36 cm^2. What is the length of the base of the triangle?
6. A triangle has a base of 8 cm and a height of 5 cm. What is the area of the triangle?
7. A triangle has sides of lengths 3 cm, 4 cm, and 5 cm. What is the perimeter of the triangle?
8. A triangle has an area of 50 cm^2 and a base of 15 cm. What is the height of the triangle?
9. A triangle has a perimeter of 24 cm and sides of lengths 5 cm, 7 cm, and 8 cm. What is the area of the triangle?
10. A triangle has a height of 15 cm and an area of 75 cm^2. What is the length of the base of the triangle?

1. A triangle has a base of 6 cm and a height of 8 cm. What is the area of the triangle? Area = (base * height) / 2 = (6 * 8) / 2 = 24 cm^2
2. A triangle has sides of lengths 7 cm, 9 cm, and 11 cm. What is the perimeter of the triangle? Perimeter = 7 + 9 + 11 = 27 cm
3. A triangle has an area of 30 cm^2 and a base of 10 cm. What is the height of the triangle? Area = (base * height) / 2 => 30 = (10 * height) / 2 => height = 30 * 2 / 10 = 6 cm
4. A triangle has a perimeter of 20 cm and sides of lengths 4 cm, 7 cm, and 9 cm. What is the area of the triangle? We cannot determine the area of the triangle from this information alone, because we do not know the height of the triangle.
5. A triangle has a height of 12 cm and an area of 36 cm^2. What is the length of the base of the triangle? Area = (base * height) / 2 => 36 = (base * 12) / 2 => base = 72 / 12 = 6 cm
6. A triangle has a base of 8 cm and a height of 5 cm. What is the area of the triangle? Area = (base * height) / 2 = (8 * 5) / 2 = 20 cm^2
7. A triangle has sides of lengths 3 cm, 4 cm, and 5 cm. What is the perimeter of the triangle? Perimeter = 3 + 4 + 5 = 12 cm
8. A triangle has an area of 50 cm^2 and a base of 15 cm. What is the height of the triangle? Area = (base * height) / 2 => 50 = (15 * height) / 2 => height = 50 * 2 / 15 = 10 cm
9. A triangle has a perimeter of 24 cm and sides of lengths 5 cm, 7 cm, and 8 cm. What is the area of the triangle? We cannot determine the area of the triangle from this information alone, because we do not know the height of the triangle.
10. A triangle has a height of 15 cm and an area of 75 cm^2. What is the length of the base of the triangle? Area = (base * height) / 2 => 75 = (base * 15) / 2 => base = 75 * 2 / 15 = 10 cm
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