### All Common Core: 7th Grade Math Resources

## Example Questions

### Example Question #11 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

Calculate the area of the provided figure.

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to recall the area formula for a triangle:

Now that we have the correct formula, we can substitute in our known values and solve:

### Example Question #11 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

What is the area of the triangle pictured above?

**Possible Answers:**

60

24

30

40

12

**Correct answer:**

24

The area of a triangle is calculated using the formula . Importantly, the height is a perpendicular line between the base and the opposite point. In a right triangle like this one, you're in luck: the triangle as drawn already has that perpendicular line as one of the two sides. So here we will calculate . That gives us an answer of 24.

### Example Question #1 : Solve For Area Of A Triangle

In triangle ABC above, the distance between point A and point D is 10 inches, and the area of the triangle is 20 square inches. What is the length of side BC?

**Possible Answers:**

2 inches

There is not enough information to answer the question

10 inches

8 inches

4 inches

**Correct answer:**

4 inches

The area of a triangle can be calculated using the formula Area = 1/2 * Base * Height. Here you're given two of the unknowns in that formula:

Area = 20

Height = 10

So you can plug those into the area formula to solve for Base, the only remaining unknown:

20 = 1/2 * Base * 10

That means that 20 = 5 * Base, so Base = 4.

### Example Question #1 : Solve For Area Of A Triangle

In triangle ABC, side BC measures 12 meters, and the shortest straight-line distance between point A and side BC is 5 meters long. What is the area of triangle ABC?

**Possible Answers:**

24

36

60

30

12

**Correct answer:**

30

The area of a triangle can be calculated using the formula . The height of a triangle is a perpendicular line connecting the base and its opposite point; in any acute or right triangle - a triangle with no angles greater than 90 degrees - the height is also the shortest line between the base and the opposite point. Here that means that if you use BC = 12 as your base, then the distance of 5 between BC and point A is the height. That means that you can calculate the area:

### Example Question #91 : Geometry

The pictured right triangle has sides of 7, 24, and 25. What is the area of that triangle?

**Possible Answers:**

84

77

125

64

128

**Correct answer:**

84

The area of a triangle can be calculated using the formula . Note that the height of any triangle is a perpendicular line between the base and its opposite angle; in a right triangle that's very convenient, because the right angle gives you that perpendicular relationship between two sides. So you can use 24 as the base and 7 as the height here. That means that the area is: