# Intermediate Geometry : How to find the area of an acute / obtuse triangle

## Example Questions

### Example Question #11 : How To Find The Area Of An Acute / Obtuse Triangle

Find the area of the triangle. Round to the nearest tenths.

Explanation:

The formula used to find the area of the triangle is

Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the height of the triangle, which in this case is the side opposite to the known angle, and we also know the length of the hypotenuse of the smaller triangle formed by the height.

Remember that

Now, solve for the height.

Now you can find the area.

### Example Question #12 : How To Find The Area Of An Acute / Obtuse Triangle

Find the area of the triangle below. Round to the nearest tenths place.

Explanation:

The formula used to find the area of the triangle is

Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the height of the triangle, which in this case is the side opposite to the known angle, and we also know the length of the hypotenuse of the smaller triangle formed by the height.

Remember that

Now, solve for the height.

Now you can find the area.

### Example Question #13 : How To Find The Area Of An Acute / Obtuse Triangle

Find the area of the triangle below. Round to the nearest tenths place.

Explanation:

The formula used to find the area of the triangle is

Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the height of the triangle, which in this case is the side opposite to the known angle, and we also know the length of the hypotenuse of the smaller triangle formed by the height.

Remember that

Now, solve for the height.

Now you can find the area.

### Example Question #14 : How To Find The Area Of An Acute / Obtuse Triangle

Find the area of the triangle below. Round to the nearest tenths place.

Explanation:

The formula used to find the area of the triangle is

Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the height of the triangle, which in this case is the side opposite to the known angle, and we also know the length of the hypotenuse of the smaller triangle formed by the height.

Remember that

Now, solve for the height.

Now you can find the area.

### Example Question #15 : How To Find The Area Of An Acute / Obtuse Triangle

In the figure, a triangle that shares its base with the width of the rectangle has a height that is half the length of the rectangle. Find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we must first find the areas of the triangle and the rectangle.

Recall how to find the area of a rectangle:

Substitute in the given length and width to find the area.

Next, recall how to find the area of a triangle:

From the question, we know that the height of the triangle is half the length of the rectangle. Use the length of the rectangle to find the height of the triangle:

Since the base of the triangle and the width of the rectangle are the same, we can find the area of the triangle:

To find the area of the shaded region, subtract the area of the triangle from the area of the rectangle.

Solve.

### Example Question #16 : How To Find The Area Of An Acute / Obtuse Triangle

In the figure, a triangle that shares its base with the width of the rectangle has a height that is half the length of the rectangle. Find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we must first find the areas of the triangle and the rectangle.

Recall how to find the area of a rectangle:

Substitute in the given length and width to find the area.

Next, recall how to find the area of a triangle:

From the question, we know that the height of the triangle is half the length of the rectangle. Use the length of the rectangle to find the height of the triangle:

Since the base of the triangle and the width of the rectangle are the same, we can find the area of the triangle:

To find the area of the shaded region, subtract the area of the triangle from the area of the rectangle.

Solve.

### Example Question #17 : How To Find The Area Of An Acute / Obtuse Triangle

In the figure, a triangle that shares its base with the width of the rectangle has a height that is half the length of the rectangle. Find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we must first find the areas of the triangle and the rectangle.

Recall how to find the area of a rectangle:

Substitute in the given length and width to find the area.

Next, recall how to find the area of a triangle:

From the question, we know that the height of the triangle is half the length of the rectangle. Use the length of the rectangle to find the height of the triangle:

Since the base of the triangle and the width of the rectangle are the same, we can find the area of the triangle:

To find the area of the shaded region, subtract the area of the triangle from the area of the rectangle.

Solve.

### Example Question #18 : How To Find The Area Of An Acute / Obtuse Triangle

In the figure, a triangle that shares its base with the width of the rectangle has a height that is half the length of the rectangle. Find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we must first find the areas of the triangle and the rectangle.

Recall how to find the area of a rectangle:

Substitute in the given length and width to find the area.

Next, recall how to find the area of a triangle:

From the question, we know that the height of the triangle is half the length of the rectangle. Use the length of the rectangle to find the height of the triangle:

Since the base of the triangle and the width of the rectangle are the same, we can find the area of the triangle:

To find the area of the shaded region, subtract the area of the triangle from the area of the rectangle.

Solve.

### Example Question #19 : How To Find The Area Of An Acute / Obtuse Triangle

In the figure, a triangle that shares its base with the width of the rectangle has a height that is half the length of the rectangle. Find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we must first find the areas of the triangle and the rectangle.

Recall how to find the area of a rectangle:

Substitute in the given length and width to find the area.

Next, recall how to find the area of a triangle:

From the question, we know that the height of the triangle is half the length of the rectangle. Use the length of the rectangle to find the height of the triangle:

Since the base of the triangle and the width of the rectangle are the same, we can find the area of the triangle:

To find the area of the shaded region, subtract the area of the triangle from the area of the rectangle.

Solve.

### Example Question #20 : How To Find The Area Of An Acute / Obtuse Triangle

In the figure, a triangle that shares its base with the width of the rectangle has a height that is half the length of the rectangle. Find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we must first find the areas of the triangle and the rectangle.

Recall how to find the area of a rectangle:

Substitute in the given length and width to find the area.

Next, recall how to find the area of a triangle:

From the question, we know that the height of the triangle is half the length of the rectangle. Use the length of the rectangle to find the height of the triangle:

Since the base of the triangle and the width of the rectangle are the same, we can find the area of the triangle:

To find the area of the shaded region, subtract the area of the triangle from the area of the rectangle.

Solve.