I need help with figure E
Find the areas of the following figures.
FIGURE A = 24?
a rhombus with a perimeter of 20 meters and a diagonal of 8 meters
FIGURE B = 120?
a rhombus with a perimeter of 52 meters and a diagonal of 24 meters
FIGURE C = 10.83?
an equilateral triangle with a perimeter of
15 meters
FIGURE D = 1387.2?
scalene triangle with sides that measure 34, 81.6, and 88.4 meters and height of 24 meters
FIGURE E: ?
an isosceles trapezoid
with a perimeter of 52 meters; one base is 10 meters greater than the other base; the measure of each leg is 3 less than twice the base of the shorter base
Is figure E 156?
figure A
since you have a rhombus with perimeter of 20, each side must be 5
Make a sketch, drawing in the two diagonals.
diagonals bisect each other, so you get 4 congruent right-angled triangles.
Consider one of them, let the missing half-diagonal be x
so x^2 + 4^2 = 5^2
x = 3 , (perhaps you recognized the 3-4-5 right-angled triangle right away ? )
so the second diagonal has length 6
Area of rhombus = product of the two diagonals/2
= 6(8)/2 = 24 units^2
good job!
Figure B = 120, correct
figure C , again correct!
figure D, correct, BUT .... the height cannot be 24, and we don't even need the height.
I found the angle opposite the smallest side to be appr 22.62° , and then used:
Area = (1/2)(81.6)(88.4)sin22.62 = appr 1387.2 , which is your answer.
so 1387.2/(81.6/2) ≠ 24
and 1387.2/(88.4/2 ≠ 24
figure E ....
I found the two parallel sides to be 8 and 18, and each of the two legs 13 , and with some basic geometry I also got 156 units^2 as the area
VERY GOOD! , all are correct
To find the area of Figure E, an isosceles trapezoid with a perimeter of 52 meters and specific base and leg measurements, you can follow these steps:
1. Understand the properties of an isosceles trapezoid: An isosceles trapezoid has two parallel bases and two equal non-parallel sides (legs). It can be broken down into a rectangle and two right triangles.
2. Identify the given information: The perimeter of the trapezoid is 52 meters, and one base is 10 meters greater than the other base. The legs (non-parallel sides) have a length that is 3 less than twice the length of the shorter base.
3. Assign variables: Let's represent the shorter base as 'x.' According to the given information, the longer base will be 'x + 10' meters. The length of each leg can be represented as '2x - 3' meters.
4. Set up the equation for the perimeter: The perimeter of the trapezoid is the sum of all sides. In this case, it is given as 52 meters:
x + (x + 10) + 2(2x - 3) + 2(2x - 3) = 52
5. Solve the equation: Simplify and solve for 'x':
x + x + 10 + 4x - 6 + 4x - 6 = 52
10x - 2 = 52
10x = 54
x = 5.4
6. Calculate the lengths of the bases and legs: Based on the value of 'x,' the first base would be 5.4 meters, and the second base would be 15.4 meters (5.4 + 10). The length of each leg would be (2 * 5.4) - 3 = 10.8 - 3 = 7.8 meters.
7. Find the height of the trapezoid: Since the trapezoid is isosceles, the height is the same as the height of either of the two right triangles formed by the legs. However, the height is not directly given in the question. To find it, we need additional information.
If you have access to supplementary diagrams or measurements, check if any other information is provided about the height. Alternatively, you can use relevant trigonometric formulas or relations within the trapezoid to determine the height.
If no additional information is given, it is not possible to determine the area of the trapezoid without making assumptions or estimating the height.
Once you have determined the height, you can calculate the area of the trapezoid using the formula: Area = (base1 + base2) * height / 2, where base1 and base2 are the lengths of the bases, and the height is the perpendicular distance between the bases.
Remember, without the height value, it is not possible to calculate the area accurately.