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

Example Questions

Example Question #21 : 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 #22 : 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 #23 : 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 #24 : 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 #25 : 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 #26 : 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 #27 : How To Find The Area Of An Acute / Obtuse Triangle

A triangle is placed in a parallelogram so they share a base.

If the height of the triangle is half that of the parallelogram, find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we will need to find the areas of the triangle and of the parallelogram.

First, recall how to find the area of a parallelogram.

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

Now, find the height of the triangle.

Plug this value in to find the area of the triangle.

Subtract the two areas to find the area of the shaded region.

Example Question #28 : How To Find The Area Of An Acute / Obtuse Triangle

A triangle is placed in a parallelogram so that they share a base.

If the height of the triangle is one-fifth of that of the parallelogram, find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we will need to find the areas of the triangle and of the parallelogram.

First, recall how to find the area of a parallelogram.

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

Now, find the height of the triangle.

Plug this value in to find the area of the triangle.

Subtract the two areas to find the area of the shaded region.

Example Question #29 : How To Find The Area Of An Acute / Obtuse Triangle

A triangle is placed so that it shares a base with a parallelogram.

If the height of the triangle is one-third that of the parallelogram, find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we will need to find the areas of the triangle and of the parallelogram.

First, recall how to find the area of a parallelogram.

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

Now, find the height of the triangle.

Plug this value in to find the area of the triangle.

Subtract the two areas to find the area of the shaded region.

Example Question #30 : How To Find The Area Of An Acute / Obtuse Triangle

A triangle is placed in a parallelogram so that they share a base.

If the height of the triangle is half that of the parallelogram, find the area of the shaded region.

Explanation:

In order to find the area of the shaded region, we will need to find the areas of the triangle and of the parallelogram.

First, recall how to find the area of a parallelogram.

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

Now, find the height of the triangle.

Plug this value in to find the area of the triangle.

Subtract the two areas to find the area of the shaded region.