Question

PLEASE HELP What is the area of a trapezoid ABCD with bases AB and CD , if: a AB = 10 cm, BC=DA=13 cm, CD=20 cm;

Answer 1

Answer:

180 square cm.

Step-by-step explanation:

We have been given that trapezoid ABCD has bases AB and CD. We are asked to find the area of our given trapezoid.

Since legs of trapezoid are equal, so our trapezoid will be an isosceles trapezoid.

As length of side AB is 10 cm, so if we draw a perpendicular from point B to side CD, it will form a right triangle.

$\text{Height}^2=13^2-5^2$

$\text{Height}^2=169-25$

$\text{Height}^2=144$

$\text{Height}=\sqrt{144}$

$\text{Height}=12$  

$\text{Area of trapezoid}=\frac{a+b}{2}\times h$

$\text{Area of trapezoid}=\frac{10+20}{2}\times 12$

$\text{Area of trapezoid}=\frac{30}{2}\times 12$

$\text{Area of trapezoid}=15\times 12$  

$\text{Area of trapezoid}=180$

Therefore, the area of our given trapezoid is 180 square cm.

Answer 2

According to the given data our trapezoid is consists of three equilateral triangles.

We can calculate the height of one triangle, which is at the same time height of the trapezoid,  using Pythagorean theorem

h=√(13∧2-5∧2)= √(169-25)= √144=12

Formula for the area of the trapezoid is

A=(a+b)/2 * h= (20+10)/2*12= 15*12=180cm∧2

Good luck!!!