Question

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

Answer 1

Is figure E 156?

Answer 2

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