The lengths of the bases in isosceles rapezoid ABDC are 7 inches and 17 inches and the measure of each
of the base angles is 45° as shown below.
7
D
E
B
A
17
MzA=mZB = 45°
Find the distance between the two bases. Explain how you know.
Find length of BD.
Find the perimeter of the trapezoid.
.
.
Express your answer in exact form using the appropriate units. Show your work.
Enter your answers, explanation, and perimeter below.

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vintechnology vintechnology · Answer 1 · 2021-12-31T17:27:27+01:00

a. The distance between the two bases of the trapezoid is 5 inches.

b. The length of the sides BD of the trapezoid is 5√2 inches

c. The perimeter of the trapezoid is 24 + 10√2 inches

m∠A = m∠B = 45°

The distance between the two bases is the height of the trapezium.

The trapezium is isosceles. Therefore,

BE = 1 / 2 (17 - 7) = 1 / 2 × 10 = 5 inches.

let

h = distance between the two bases.

Using trigonometric ratio,

tan 45° = opposite / adjacent

tan 45° = h / 5

h = 5 tan 45°

h = 5 inches

The length BD can be found using Pythagoras theorem.

Therefore,

BD² = 5² + 5²

BD = √50

BD = 5√2 inches

The perimeter of the trapezium is the sum of all it sides. Therefore,

perimeter = 17 + 7 + 5√2 + 5√2

perimeter = 24 + 10√2 inches

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