ABCD is a quadrilateral with BC perpendicular to AB and DE is perpindicular to AB. If AB is 38 yard and EB equals 18 yards, BC equals 13 yards, and DE equals 15 yards. Find the area of ABCD
first of all, i don't know if there is a figure given in your question,, but if there is not, you have to imagine,,
it is composed of a trapezoid EBCD and triangle AED,, therefore,
Area,trapezoid = (b1+b2)*h/2
Area,triangle = bh/2
A,trap = (13+15)*18/2 = 252 sq yards
A,tri = (20*15)/2 = 150 sq yards
**note that 20 came from 38-18
therefore,
A,quad = 252+150 = 402 sq yards
so there,, :)
To find the area of the quadrilateral ABCD, you can use the formula for the area of a trapezoid since the given information describes a trapezoid.
The formula for the area of a trapezoid is A = (1/2)(b1 + b2)(h), where b1 and b2 are the lengths of the parallel bases, and h is the height (the perpendicular distance between the two bases).
In this case, AB is considered the longer base (b1) and DE is considered the shorter base (b2). The perpendicular distance between the bases is BC.
Given:
AB = 38 yards (b1)
EB = 18 yards (part of b1)
BC = 13 yards (h)
DE = 15 yards (b2)
To find the length of AB without EB:
AB = EB + BE = 18 + 20 = 38 yards
Now, let's calculate the area of trapezoid ABCD:
A = (1/2)(AB + DE)(BC)
Substituting the given values:
A = (1/2)(38 + 15)(13)
A = (1/2)(53)(13)
A = (1/2)(689)
A = 344.5 square yards
Therefore, the area of quadrilateral ABCD is 344.5 square yards.