The total area of the polygon can be calculated by finding the area of the triangle and the rectangle separately and then adding them together.
Area of the triangle = 1/2 * base * height
Area of the triangle = 1/2 * (4+4) * 6
Area of the triangle = 4 * 6
Area of the triangle = 24 square units
Area of the rectangle = length * width
Area of the rectangle = 4 * 6
Area of the rectangle = 24 square units
Total area of the polygon = Area of triangle + Area of rectangle
Total area of the polygon = 24 + 24
Total area of the polygon = 48 square units
Therefore, the area of the polygon is 48 square units.
Question
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
7 answers
nope, good try though
Let's try again:
To find the total area of the polygon, we need to calculate the area of the triangle and the rectangle separately and then add them together.
Area of the triangle:
Base of the triangle = 4 + 4 = 8
Height of the triangle = 6
Area of the triangle = 1/2 * base * height
Area of the triangle = 1/2 * 8 * 6
Area of the triangle = 24 square units
Area of the rectangle:
Length of the rectangle = 4
Width of the rectangle = 6
Area of the rectangle = length * width
Area of the rectangle = 4 * 6
Area of the rectangle = 24 square units
Total area of the polygon = Area of triangle + Area of rectangle
Total area of the polygon = 24 + 24
Total area of the polygon = 48 square units
Therefore, the correct area of the polygon is 48 square units.
To find the total area of the polygon, we need to calculate the area of the triangle and the rectangle separately and then add them together.
Area of the triangle:
Base of the triangle = 4 + 4 = 8
Height of the triangle = 6
Area of the triangle = 1/2 * base * height
Area of the triangle = 1/2 * 8 * 6
Area of the triangle = 24 square units
Area of the rectangle:
Length of the rectangle = 4
Width of the rectangle = 6
Area of the rectangle = length * width
Area of the rectangle = 4 * 6
Area of the rectangle = 24 square units
Total area of the polygon = Area of triangle + Area of rectangle
Total area of the polygon = 24 + 24
Total area of the polygon = 48 square units
Therefore, the correct area of the polygon is 48 square units.
Use the image to answer the question.
A polygon shows an outline in the shape of a house with a triangular roof, a door and a chimney, standing on two base pillars. The length of the two rectangular pillars is 4 and the width is 3. The gap between the two pillars, or the door, measures 2 across and the inner side of the vertical pillars measures 3.5. The perpendicular height of the triangular roof is 6. The sides of the triangle base extending outward from the outer side of both pillars is 2. The sides of the chimney sitting on the slanted roof on the right measure 1 and 2 and its thickness is 1.
Find the area of the polygon. Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
(1 point)
Responses
50.5 square units
50.5 square units
61 square units
61 square units
62.5 square units
62.5 square units
61.5 square units
A polygon shows an outline in the shape of a house with a triangular roof, a door and a chimney, standing on two base pillars. The length of the two rectangular pillars is 4 and the width is 3. The gap between the two pillars, or the door, measures 2 across and the inner side of the vertical pillars measures 3.5. The perpendicular height of the triangular roof is 6. The sides of the triangle base extending outward from the outer side of both pillars is 2. The sides of the chimney sitting on the slanted roof on the right measure 1 and 2 and its thickness is 1.
Find the area of the polygon. Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
(1 point)
Responses
50.5 square units
50.5 square units
61 square units
61 square units
62.5 square units
62.5 square units
61.5 square units
To find the area of the polygon, we need to break it down into different shapes and calculate the area of each shape.
1. Rectangle (pillar):
- Length = 4
- Width = 3
Area of the rectangle = Length * Width = 4 * 3 = 12 square units (for each pillar, total for 2 pillars = 24 square units)
2. Door:
- Width = 2
- Height (distance between the pillars) = 3.5
Area of the door = 2 * 3.5 = 7 square units
3. Triangle (roof):
- Base = 2 + 4 + 2 = 8 (sum of sides extending from pillars)
- Height = 6
Area of the triangle = 1/2 * Base * Height = 1/2 * 8 * 6 = 24 square units
4. Chimney:
- Height = 1
- Base = 2
Area of the chimney = 1 * 2 = 2 square units
Total area = Area of pillars + Area of door + Area of roof + Area of chimney
Total area = 24 + 7 + 24 + 2 = 57 square units
Therefore, the area of the polygon is 57 square units.
1. Rectangle (pillar):
- Length = 4
- Width = 3
Area of the rectangle = Length * Width = 4 * 3 = 12 square units (for each pillar, total for 2 pillars = 24 square units)
2. Door:
- Width = 2
- Height (distance between the pillars) = 3.5
Area of the door = 2 * 3.5 = 7 square units
3. Triangle (roof):
- Base = 2 + 4 + 2 = 8 (sum of sides extending from pillars)
- Height = 6
Area of the triangle = 1/2 * Base * Height = 1/2 * 8 * 6 = 24 square units
4. Chimney:
- Height = 1
- Base = 2
Area of the chimney = 1 * 2 = 2 square units
Total area = Area of pillars + Area of door + Area of roof + Area of chimney
Total area = 24 + 7 + 24 + 2 = 57 square units
Therefore, the area of the polygon is 57 square units.
50.5 square units
50.5 square units
pick through these and re-do your work
61 square units
61 square units
62.5 square units
62.5 square units
61.5 square units
50.5 square units
pick through these and re-do your work
61 square units
61 square units
62.5 square units
62.5 square units
61.5 square units
Let's correct the calculations:
1. Area of two rectangular pillars:
- Length = 4
- Width = 3
Area of each pillar = Length * Width = 4 * 3 = 12 square units
Total area for two pillars = 2 * 12 = 24 square units
2. Area of the door:
- Width = 2
- Height = 3.5
Area of the door = Width * Height = 2 * 3.5 = 7 square units
3. Area of the triangular roof:
- Base = 2 + 4 + 2 = 8
- Height = 6
Area of the triangle = 1/2 * Base * Height = 1/2 * 8 * 6 = 24 square units
4. Area of the chimney:
- Base = 1
- Height = 2
Area of the chimney = Base * Height = 1 * 2 = 2 square units
Total area = Area of pillars + Area of door + Area of roof + Area of chimney
Total area = 24 + 7 + 24 + 2 = 57 square units
Therefore, the area of the polygon is 57 square units.
1. Area of two rectangular pillars:
- Length = 4
- Width = 3
Area of each pillar = Length * Width = 4 * 3 = 12 square units
Total area for two pillars = 2 * 12 = 24 square units
2. Area of the door:
- Width = 2
- Height = 3.5
Area of the door = Width * Height = 2 * 3.5 = 7 square units
3. Area of the triangular roof:
- Base = 2 + 4 + 2 = 8
- Height = 6
Area of the triangle = 1/2 * Base * Height = 1/2 * 8 * 6 = 24 square units
4. Area of the chimney:
- Base = 1
- Height = 2
Area of the chimney = Base * Height = 1 * 2 = 2 square units
Total area = Area of pillars + Area of door + Area of roof + Area of chimney
Total area = 24 + 7 + 24 + 2 = 57 square units
Therefore, the area of the polygon is 57 square units.