1. The area of a kite is 240 cm? and the length of one diagonal is 40 cm. How long is the other
diagonal?
2. The length of one base of a trapezoid is 18 cm while the length of the median is 12 cm. Find the length of the other base.
3. If one of the base angles in an isosceles trapezoid is represented by (x)° and the other base
is (3x- 70)°, what are the measures of the angles in the isosceles trapezoid?
1. Area of a "kite" = product of the diagonals / 2
2. length of the median of a trapezoid = (sum of the parallel sides) / 2
3. In an isosceles triangle, the two base angles are equal.
so in your triangle:
3x - 70 = x
solve for x, then use the fact that all 3 angles add up to 180° to find the
third angle.
1. To find the length of the other diagonal of a kite, we can use the formula for the area of a kite:
Area = 1/2 * (product of diagonals)
Given that the area is 240 cm² and one diagonal is 40 cm, we can substitute these values into the formula to solve for the other diagonal:
240 = 1/2 * 40 * (length of other diagonal)
Simplifying the equation:
240 = 20 * (length of other diagonal)
Dividing both sides by 20:
12 = length of other diagonal
Therefore, the length of the other diagonal is 12 cm.
2. In a trapezoid, the median is the average of the two bases.
Given that one base is 18 cm and the median is 12 cm, we can set up the following equation:
12 = (18 + length of other base) / 2
Multiplying both sides by 2:
24 = 18 + length of other base
Subtracting 18 from both sides:
6 = length of other base
Therefore, the length of the other base is 6 cm.
3. In an isosceles trapezoid, opposite angles are equal. Let's represent the base angle as x° and the other base angle as (3x-70)°.
Since opposite angles in an isosceles trapezoid are equal, we can set up the following equation:
x = 3x - 70
Adding 70 to both sides:
x + 70 = 3x
Subtracting x from both sides:
70 = 2x
Dividing both sides by 2:
35 = x
Therefore, one of the base angles is 35°. Since opposite angles are equal, the other base angle is also 35°.
Hence, the measures of the angles in the isosceles trapezoid are: base angles = 35°, and other base angles = 35°.
1. To find the length of the other diagonal of a kite, we can use the formula for the area of a kite. The formula is A = d1 * d2 / 2, where A is the area and d1 and d2 are the lengths of the diagonals. In this case, we know that the area is 240 cm² and one diagonal is 40 cm. We can rearrange the formula to solve for the other diagonal.
Let d2 be the length of the other diagonal.
240 cm² = 40 cm * d2 / 2
Multiplying both sides by 2:
480 cm² = 40 cm * d2
Dividing both sides by 40 cm:
12 cm = d2
Therefore, the length of the other diagonal is 12 cm.
2. In a trapezoid, the median is the line segment that connects the midpoints of the two legs. We can use the formula for the median length: median = (base1 + base2) / 2. In this case, we know that the length of one base is 18 cm and the length of the median is 12 cm. We can rearrange the formula to solve for the length of the other base.
Let b2 be the length of the other base.
12 cm = (18 cm + b2) / 2
Multiplying both sides by 2:
24 cm = 18 cm + b2
Subtracting 18 cm from both sides:
6 cm = b2
Therefore, the length of the other base is 6 cm.
3. In an isosceles trapezoid, the base angles are congruent. We know that one base angle is represented by (x)° and the other base is (3x - 70)°. We can set up an equation to find the value of x and then use it to find the measures of the angles.
Since the base angles are congruent, we can set up an equation:
x° = 3x - 70°
Adding 70° to both sides:
x° + 70° = 3x
Subtracting x° from both sides:
70° = 2x
Dividing both sides by 2:
35° = x
Now that we have the value of x, we can substitute it back into the expressions to find the angles:
One base angle = (35)°
Other base angle = 3x - 70 = 3(35) - 70 = 105° - 70° = 35°
Therefore, the measures of the angles in the isosceles trapezoid are 35° and 35°.