Use the image to answer the question.
An illustration shows the outline of a rightward facing arrow head. The perpendicular height of the triangular part is 6. The sides of the rectangular part each measure 4. The part of the triangle's base on either side of the rectangular part measures 4.
Find the area of the polygon in square units.
(1 point)
square units
To find the area of the polygon, we will first find the area of the triangular part and the area of the rectangular part, and then add them together.
1. Area of the triangular part:
The perpendicular height of the triangular part is given as 6 units, and the width of the triangular base on either side of the rectangular part is 4 units. Since the triangular part is a right-angled triangle, we can use the formula for the area of a triangle:
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 4 * 6
Area of triangle = 12 square units
2. Area of the rectangular part:
The length of one side of the rectangular part is 4 units, and since the rectangular part is a rectangle, we can use the formula for the area of a rectangle:
Area of rectangle = length * width
Area of rectangle = 4 * 4
Area of rectangle = 16 square units
3. Total area of the polygon:
To find the total area of the polygon, we add the area of the triangular part and the area of the rectangular part:
Total area = Area of triangle + Area of rectangle
Total area = 12 + 16
Total area = 28 square units
Therefore, the area of the polygon is 28 square units.
To find the area of the polygon, we need to first calculate the area of each individual shape within the polygon and then sum them up.
The polygon in the image consists of a triangle and a rectangle.
Let's calculate the area of each shape:
1. Triangle:
The formula for the area of a triangle is (base x height) / 2.
In this case, the base of the triangle is the sum of the lengths of the parts of the triangle's base on either side of the rectangular part, which is 4 + 4 = 8. The height of the triangle is given as 6.
So, the area of the triangle is (8 x 6) / 2 = 48 / 2 = 24 square units.
2. Rectangle:
The formula for the area of a rectangle is length x width.
In this case, both the length and width of the rectangular part are given as 4.
So, the area of the rectangle is 4 x 4 = 16 square units.
Now, to find the total area of the polygon, we add the areas of the triangle and the rectangle together:
Total area = Area of triangle + Area of rectangle = 24 + 16 = 40 square units.
Therefore, the area of the polygon is 40 square units.
The polygon consists of a rectangle and two congruent right triangles. The area of the rectangle is 4 x 6 = 24 square units. The area of each right triangle is 1/2 x base x height, which is 1/2 x 4 x 6 = 12 square units. Therefore, the total area of the polygon is 24 + 12 + 12 = 48 square units.
Answer: 48 square units.