A piece of a tile is in the shape of a right triangle. The base is 112 centimeters and the height is 212 centimeters. What is the area in square centimeters?
The area of a parallelogram is given by the formula:
A = bh
where A is the area, b is the base (one of the sides), and h is the height (the length of the perpendicular line between the base and the opposite side).
In this case, the base is the top side of length 10 centimeters, and the height is the length of the perpendicular line from the top left vertex to the bottom side, which is 8 centimeters. Plugging these values into the formula, we get:
A = (10 cm)(8 cm)
A = 80 square centimeters
Therefore, the area of the quadrilateral is 80 square centimeters.
The area of a parallelogram is given by the formula:
A = bh
where A is the area, b is the base (one of the sides), and h is the height (the length of the perpendicular line between the base and the opposite side).
In this case, the base is the bottom side of length 14 inches, and the height is the length of the perpendicular line from the bottom right vertex to the top side, which is 3 inches. Plugging these values into the formula, we get:
A = (14 inches)(3 inches)
A = 42 square inches
Therefore, the area of the quadrilateral is 42 square inches.
The area of a triangle is given by the formula:
A = (1/2)bh
where A is the area, b is the base, and h is the height. Plugging in the values given, we get:
A = (1/2)(112cm)(212cm) = 11,904 cm^2
Therefore, the area of the triangle is 11,904 square centimeters.
What is the area of the non-right triangle? The base and height are found by counting the squares.
(1 point)
The area is
square units.
I'm sorry, but I cannot answer this question without more information. In order to find the area of a triangle, we need to know either the length of the base and the height, or the lengths of two sides and the included angle (if it is not a right triangle). Counting squares may give us an estimate, but it is not enough information to calculate an accurate area.
Find the area of the non-right triangle. The base and height are found by counting the squares.
(1 point)
Responses
35 square units
35 square units
32.5 square units
32.5 square units
17.5 square units
17.5 square units
65 square units
Use the image to answer the question.
An illustration shows a trapezoid with the longer side on the left labeled as 12 inches. The opposite parallel side is 10 inches. Two perpendicular dotted lines extend from the vertices at either end of the 10 inch side to the longer side, and are labeled 8 inches. The two perpendicular lines are denoted by 4 right angle symbols.
What is the area of the quadrilateral?
To find the area of the trapezoid, we can use the formula:
A = (1/2)(b1 + b2)h
where A is the area, b1 and b2 are the lengths of the parallel sides, and h is the height (the length of the perpendicular line between the parallel sides).
In this case, b1 = 12 inches, b2 = 10 inches, and h = 8 inches. Plugging these values into the formula, we get:
A = (1/2)(12 + 10)(8)
A = (1/2)(22)(8)
A = 88 square inches
Therefore, the area of the quadrilateral is 88 square inches.
Area of Special Quadrilaterals Practice
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3 of 53 of 5 Items
Question
Use the image to answer the question.
An illustration shows a parallelogram with top side as 10 centimeters. A perpendicular dotted line from top left vertex to the bottom side is 8 centimeters. The perpendicular line makes one right angle symbol with top side and two right angle symbols with the bottom side.
What is the area of the quadrilateral?
Use the image to answer the question.
An illustration shows a parallelogram with bottom side as 14 inches. A perpendicular dotted line from the bottom right vertex to the top side is 3 inches. The perpendicular line is denoted by two right angle symbols.
What is the area of the quadrilateral?
Use the image to answer the question.
An illustration shows a parallelogram with top side as 7 centimeters. A perpendicular dotted line from the top left vertex to the bottom side is 12 centimeters. The perpendicular line makes one right angle symbol with the top side and two right angle symbols with the bottom side.
What is the area of the quadrilateral?
The area of a parallelogram is given by the formula:
A = bh
where A is the area, b is the base (one of the sides), and h is the height (the length of the perpendicular line between the base and the opposite side).
In this case, the base is the top side of length 7 centimeters, and the height is the length of the perpendicular line from the top left vertex to the bottom side, which is 12 centimeters. Plugging these values into the formula, we get:
A = (7 cm)(12 cm)
A = 84 square centimeters
Therefore, the area of the quadrilateral is 84 square centimeters.
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.
First, we can find the area of the rectangular part of the house by multiplying the length and width of one of the rectangular pillars:
Area of rectangular part = length x width = 4 x 3 = 12
Next, we can find the area of the triangular part of the roof by using the formula for the area of a triangle:
Area of triangular roof = (1/2) x base x height = (1/2) x 2 x 6 = 6
To find the total area of the roof and the rectangular part, we add these two areas together. However, we need to subtract the area of the door, since it is a gap within the polygon. The area of the door can be found by multiplying its dimensions:
Area of door = length x width = 2 x 3.5 = 7
Finally, we need to add in the area of the chimney. We can view the chimney as a triangular prism, with a triangular base of area 1/2 and a thickness of 1. The height of this prism is the height of the triangular roof minus the height of the chimney base, or 6 - 1 = 5. Therefore, the volume of the chimney is:
Volume of chimney = area of base x height x thickness = (1/2) x 5 x 1 = 2.5
Adding up all of these areas and volumes, we get:
Total area = rectangular part + triangular roof - area of door + volume of chimney
Total area = 12 + 6 - 7 + 2.5
Total area = 13.5
Therefore, the area of the polygon (house) is 13.5 square units.
Area of Polygons Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows the outline of letter upper Y. The vertical rectangular base of the letter has length 7 and width 2. The outward slanting lines measure 12 on the outer side and 7 on the inner side. The thickness of the left slanting line is marked a, and that of the right is marked b. The perpendicular height from the top inner corner angle of the right slant is marked as a dashed line labeled c. The inward extension of the inner side of the left slant line down to the right corner of the rectangular base is marked with a dashed line labeled d.
Which segment would you need to know the length of in order to find the area of the polygon?
To find the area of the polygon, we need to know the dimensions of all its sides and angles. However, since the question asks which segment is needed to calculate the area, we can focus on the sides that directly contribute to the shape of the polygon, which in this case are the base and the two slanting lines.
We are given the length and width of the rectangular base, which are 7 and 2, respectively. We are also given the lengths of the two slanting lines on both sides of the Y shape, which are 12 and 7 on the outer and inner sides, respectively. Therefore, the only missing segment that we need to know in order to find the area of the polygon is either segment a or segment b, which represent the thickness of the left and right slanting lines, respectively.
Without knowing the value of either a or b, we cannot accurately find the area of the polygon.
Use the image to answer the question.
An illustration shows the outline of letter upper T. The vertical rectangular base of the letter has length 12 and width 3. The horizontal rectangular crossbar at the top has thickness 2. The lower sides of the horizontal crossbar on either side of the vertical base measure 4.
What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
To find the area of the polygon, we can break it down into two rectangles. The first rectangle is the vertical base, which has length 12 and width 3:
Area of vertical rectangle = length x width = 12 x 3 = 36
The second rectangle is the horizontal crossbar, which has length 12 (the same as the base) and width 2:
Area of horizontal rectangle = length x width = 12 x 2 = 24
Since the crossbar only overlaps with the vertical base in the middle, we need to subtract the area of this overlap to avoid double-counting. The overlap has a width of 3 (the same as the width of the base), and a length of 2 (the thickness of the crossbar). Therefore, the area of the overlap is:
Area of overlap = length x width = 2 x 3 = 6
The total area of the polygon is the sum of the areas of the two rectangles minus the area of the overlap:
Total area = area of vertical rectangle + area of horizontal rectangle - area of overlap
Total area = 36 + 24 - 6
Total area = 54
Therefore, the area of the polygon is 54 square units.
Use the image to answer the question.
A polygon is drawn in the shape of the outline of an upward facing arrowhead, where the base is bent inward, leaving two triangular edges at the base. The perpendicular height of the triangular arrowhead is 3. The sides of the rectangular part measure 4 plus 2. The part of the arrowhead triangle’s base extending outward on both sides of the rectangular measures 1. The bases of the triangular edges each measure 3 and are indicated by a dashed horizontal line drawn from edge to edge of the rectangle, sitting on the inward point at the base of the polygon.
What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
To find the area of the polygon, we can break it down into two triangles and a rectangle.
First, let's focus on the rectangle in the middle. We are given that its sides measure 4 and 2, so its area is:
Area of rectangle = length x width = 4 x 2 = 8
Next, let's look at one of the triangles at the base. We are given that the base of each triangle measures 3 and that the height of the entire arrowhead is 3. Therefore, the area of one of the triangles is:
Area of triangle = (1/2) x base x height = (1/2) x 3 x 3 = 4.5
Since the polygon has two of these triangles, we need to double this area to account for both:
Total area of triangles = 2 x 4.5 = 9
Now we need to find the area of the part of the arrowhead triangle’s base extending outward on both sides of the rectangle. We are given that each side of this base measures 1, so the total length of the base is 2. Since the height of this part is also 3, the area is:
Area of side triangles = (1/2) x base x height = (1/2) x 2 x 3 = 3
Adding together the areas of the rectangle and the triangles, and subtracting the area of the side triangles (since they overlap with the other shapes), we get:
Total area = area of rectangle + total area of triangles - area of side triangles
Total area = 8 + 9 - 3
Total area = 14
Therefore, the area of the polygon is 14 square units.
Area of Polygons Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration shows the outline of letter X. The length of each of the four legs is 7, and the width of each is 5.
What is the area of the polygon? Assume that segments that appear congruent are congruent.
Each of the four legs of the X is a rectangle with a length of 7 and a width of 5. Therefore, the area of one of these rectangles is:
Area of rectangle = length x width = 7 x 5 = 35
Since there are four of these rectangles, the total area covered by the X is:
Total area = 4 x area of rectangle
Total area = 4 x 35
Total area = 140
Therefore, the area of the polygon is 140 square units.