### All ACT Math Resources

## Example Questions

### Example Question #181 : Plane Geometry

If the area of an isosceles triangle is and its base is , what is the height of the triangle?

**Possible Answers:**

**Correct answer:**

Use the formula for area of a triangle to solve for the height:

### Example Question #182 : Plane Geometry

Find the height of the isosceles triangle above if the length of and . If your answer is in a decimal form, round to the nearest tenths place.

**Possible Answers:**

**Correct answer:**

Because this is an isosceles triangle, . Also, we know that the base of the triangle, . Therefore, we create two triangles by bisecting the trinagle down the center. We are solving for the length of the long arm of the triangle. We know that the hypotenuse is 12 and the base is 4 (half of 8).

Thus we use the Pythagorean Theorem to find the length of the long arm:

### Example Question #183 : Plane Geometry

The triangle above has an area of units squared. If the length of the base is units, what is the height of the triangle?

**Possible Answers:**

**Correct answer:**

The area of a triangle is found using the formula

The height of any triangle is the length from it's highest point to the base, as pictured below:

We can find the height by rearranging the area formula: