To find the area of the quadrilateral, we need to find the area of the trapezoid and the area of the right triangle within it.
First, find the area of the trapezoid:
Area of a trapezoid = (1/2) * (sum of parallel sides) * height
= (1/2) * (4 + 6) * 9
= (1/2) * 10 * 9
= 45 square centimeters
Next, find the area of the right triangle within the trapezoid:
Area of a right triangle = (1/2) * base * height
= (1/2) * 4 * 3
= 6 square centimeters
Therefore, the total area of the quadrilateral is 45 square centimeters + 6 square centimeters = 51 square centimeters.
Use the image to answer the question.
An illustration shows a trapezoid with top side as 4 centimeters, and the left as the longest side of 9 centimeters. The opposite parallel side on the right is 6 centimeters. A diagonal bottom side is 5 centimeters. The top side is perpendicular to the left and right sides as denoted by right two angle symbols. A perpendicular dotted line from the bottom right vertex to the left side is drawn. The dotted line makes one right angle symbol with right side and two right angle symbols with the left side. It forms a right triangle at the bottom of the trapezoid, with the 5 centimeter side as the hypotenuse.
Find the area of the quadrilateral.
(1 point)
3 answers
wrong @bot
Apologies for the mistake in the previous response. Let's correct it.
Given:
- Top side length = 4 cm
- Left side length = 9 cm
- Right side length = 6 cm
- Diagonal (bottom side) length = 5 cm
To find the area of the quadrilateral:
1. Split the trapezoid into a rectangle and a right triangle by drawing the perpendicular dotted line from the bottom right vertex to the left side.
2. The right triangle has a base of 4 cm (from the top side) and a height of 3 cm (remaining height of the trapezoid after subtraction).
Area of the right triangle = (1/2)*base*height
Area = (1/2)*Complimentary base*height
Area = (1/2)*4*3
Area = 6 square centimeters
3. The remaining shape is a rectangle with a base of 6 cm (from the right parallel side) and a height of 3 cm (same as the right triangle).
Area of the rectangle = base*height
Area = 6*3
Area = 18 square centimeters
4. Add the area of the right triangle and the area of the rectangle to get the total area of the quadrilateral:
Total area = Area of right triangle + Area of rectangle
Total area = 6 + 18
Total area = 24 square centimeters
Therefore, the area of the quadrilateral is 24 square centimeters.
Given:
- Top side length = 4 cm
- Left side length = 9 cm
- Right side length = 6 cm
- Diagonal (bottom side) length = 5 cm
To find the area of the quadrilateral:
1. Split the trapezoid into a rectangle and a right triangle by drawing the perpendicular dotted line from the bottom right vertex to the left side.
2. The right triangle has a base of 4 cm (from the top side) and a height of 3 cm (remaining height of the trapezoid after subtraction).
Area of the right triangle = (1/2)*base*height
Area = (1/2)*Complimentary base*height
Area = (1/2)*4*3
Area = 6 square centimeters
3. The remaining shape is a rectangle with a base of 6 cm (from the right parallel side) and a height of 3 cm (same as the right triangle).
Area of the rectangle = base*height
Area = 6*3
Area = 18 square centimeters
4. Add the area of the right triangle and the area of the rectangle to get the total area of the quadrilateral:
Total area = Area of right triangle + Area of rectangle
Total area = 6 + 18
Total area = 24 square centimeters
Therefore, the area of the quadrilateral is 24 square centimeters.
1 answer