As shown in the figure, in rectangular ABCD, e is a point on CD, angle DEA = 30 degrees, and AE = AB = 8cm, find 1, degree of angle EBC, 2, area of triangle Abe

As shown in the figure, in rectangular ABCD, e is a point on CD, angle DEA = 30 degrees, and AE = AB = 8cm, find 1, degree of angle EBC, 2, area of triangle Abe

1. From the angle DEA = 30 degrees, the angle EAB = 30 degrees;
If AB = AE, the angle Abe = angle AEB = 75 degrees, and the angle BEC = 180-30-75 degrees = 75 degrees;
Push out angle EBC = 90 - 75 = 15 degrees
2. From the angle DEA = 30 degrees, we can see that ad = BC = 1 / 2Ab = 4; de = 4 √ 3; EC = 8-4 √ 3;
The area of triangle ade is: 1 / 2 * 4 * 4 √ 3 = 8 √ 3;
The area of triangle BEC is: 1 / 2 * 4 * (8-4 √ 3) = 16-8 √ 3;
The area of rectangle ABCD is 8 * 4 = 32;
The area of triangle Abe is 32-8 √ 3-16 + 8 √ 3 = 16

In the quadrilateral ABCD, e is a point on AB, triangle ade and triangle BCF are equilateral triangles, and the midpoint p q m n of AB BC CD Da is calculated as pqmn

Connect BD and AC;
∵ △ ade and △ ECB are equilateral triangles,
∴AE=DE,EC=BE,∠AED=∠BEC=60°；
∴∠AEC=∠DEB=120°；
∴△AEC≌△DEB；
∴AC=BD；
M and N are the midpoint of CD and AD,
The median line of △ ACD is Mn = 1.2 AC,
In the same way, NP = 12 dB, QP = 12 AC, MQ = 12 BD,
∴MN=NP=PQ=MQ,
The quadrilateral npqm is a diamond;
So C

The product of the upper bottom and the height of a trapezoid is 180 square centimeters, and the product of the lower bottom and the height is 200 square centimeters. What is the area of the trapezoid
Formula

Because trapezoid area = (upper bottom + lower bottom) × height △ 2
= [product of upper bottom and height (180) + product of lower bottom and height (200)] 2
So the area of this trapezoid is:
(180 + 200) △ 2 = 190 (cm2)

The product of the upper bottom and the height of a trapezoid is 180 square centimeters, and the product of the lower bottom and the height is 200 square centimeters. What is the area of this trapezoid

Trapezoidal area
=(upper bottom + lower bottom) × height △ 2
=Upper bottom × height △ 2 + lower bottom × height △ 2
=180÷2+200÷2
=90+100
=190 square centimeters

The top, bottom and height of a trapezoid are in whole centimeters. The product of the top, bottom and height is 12 and 21 respectively. The area of this trapezoid is______ Square centimeter

(12 + 21) △ 2 = 33 △ 2, = 16.5 (square centimeter); answer: the area of this trapezoid is 16.5 square centimeter

For a trapezoid, the product of its height, upper bottom and lower bottom is 17.8 square meters and 15.4 square meters respectively. The area of this trapezoid is - square meters

Let the top bottom of the trapezoid be a, the bottom B and the height H
Ah = 17.8 square meters BH = 15.4 square meters
S ladder = (a + b) h * 1 / 2
=（ah+bh）*1/2
=（17.8+15.4）*1/2
=16.6

For a trapezoid, the product of its height and two bases is equal to 16 square meters and 21 square meters respectively

Let H be the height, a be the bottom, B be the bottom, then ah = 16, BH = 21;
The area is s = 0.5 * (a + b) * H = 0.5 (ah + BH) = 0.5 * 37 = 18.5

For a trapezoid, the product of its height and upper bottom is 15 square centimeters, and the product of its height and lower bottom is 21 square centimeters. What is the area of this trapezoid

Because the trapezoid area = (upper bottom + lower bottom) × height △ 2 = [product of upper bottom and height (15) + product of lower bottom and height (21)] / 2, the trapezoid area is: (15 + 21) △ 2 = 18 (square centimeter). Thank you

A trapezoid has an area of 480 square centimeters, a height of 20 centimeters, a bottom of 18 centimeters, and a top of how many centimeters?

480 × 2 △ 20-18, = 48-18, = 30 (CM); a: the upper and bottom are 30 cm

The lower part of a trapezoid is 1 / 4 longer, and the upper part and height remain unchanged. The area of the new trapezoid is 76 square centimeters larger than that of the original trapezoid. What is the area of the original trapezoid
The top is 20 cm and the bottom is 32 cm

32 × 1 / 4 = 8 cm (extended length)
Added a triangle
76 × 2 △ 8 = 19cm (H)
The original area = (20 + 32) × 19 △ 2 = 494 square centimeters
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