Question
Two Rectangles ABCD and DBEF are as shown in the figure. The area of Rectangle DBEF is
- 10 cm2
- 12 cm2
- 14 cm2
- 15 cm2
Hint:
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. A triangle in geometry is a three-sided polygon with three edges and three vertices. Here we have given two rectangles and we have to find ABCD and DBEF and we have to find the area of Rectangle DBEF.
The correct answer is: 12 cm2
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
We have given two Rectangles ABCD and DBEF are as shown in the figure.
Now lets first find DB, we can use Pythagoras theorem to find DB, we get:
AB2+AD2=DB2
42+32=DB2
DB2=16+9
DB2=25
Taking square root on both sides, we get:
DB=5 cm.
Area of ABCD = 2 x area of BCD (ad diagonal divdes area equally)
area of BCD=3x4/2
area of BCD=6 cm2
Now we have triangle BCD, we know that if a triangle and rectangle lies on same base and is in between same parallel lines, then the area of rectangle is twice of area of triangle, so:
area of triangle BCD x 2 = area of rectangle DBEF
6 x 2 = area of rectangle DBEF
area of rectangle DBEF= 12 cm2
So here we used the concept of rectangle and triangle, and we understood the relation between them to solve this question. The total of the triangles' individual areas makes up the rectangle's surface area.So the area of rectangle DBEF is 12 cm2.
Related Questions to study
In the given figure, ABCD is a Cyclic Quadrilateral 
and 
then
In the given figure, ABCD is a Cyclic Quadrilateral and then
In the figure below 
If 
, 
and 
then which of the following is correct ?
In the figure below If , and then which of the following is correct ?
If ABCD is a square, MDC is an Equilateral Triangle. Find the value of x
So here we were given a square PQRS and in that an equilateral triangle STR is present. We used the concept of equilateral triangle to solve the answer. So the angle x is equal to 105 degrees.
If ABCD is a square, MDC is an Equilateral Triangle. Find the value of x
So here we were given a square PQRS and in that an equilateral triangle STR is present. We used the concept of equilateral triangle to solve the answer. So the angle x is equal to 105 degrees.
If PQRS is a Square and STR is an Equilateral Triangle. Find the value of a
So here we were given a square PQRS and in that an equilateral triangle STR is present. We used the concept of equilateral triangle to solve the answer. So the angle a is equal to 75 degrees.
If PQRS is a Square and STR is an Equilateral Triangle. Find the value of a
So here we were given a square PQRS and in that an equilateral triangle STR is present. We used the concept of equilateral triangle to solve the answer. So the angle a is equal to 75 degrees.
In a Trapezium ABCD, as shown, 
and 
then length of AB is
In a Trapezium ABCD, as shown, and then length of AB is
In the following diagram, the bisectors of interior angles of the Parallelogram PQRS enclose a Quadrilateral ABCD. Then find angle A.
In the following diagram, the bisectors of interior angles of the Parallelogram PQRS enclose a Quadrilateral ABCD. Then find angle A.
In a Rhombus PQRS; if 
?
In a Rhombus PQRS; if ?
In an Isosceles Trapezium PQRS, 
then find the length of PR.
In an Isosceles Trapezium PQRS, then find the length of PR.
ABCD is a square then find 'a’ in the given figure
ABCD is a square then find 'a’ in the given figure
What is the value of 'a’?
What is the value of 'a’?
Find the value of ' ' x in the following figure
Find the value of ' ' x in the following figure
In DABC, if AD is bisector 
and DE bisects 
find 
Therefore, 
is 85.
In DABC, if AD is bisector and DE bisects find
Therefore, is 85.
Find ‘b’ in the given figure
Therefore, the value of b is 125.
Find ‘b’ in the given figure
Therefore, the value of b is 125.
Find x in the given figure
Therefore, the value of x is 65.
Find x in the given figure
Therefore, the value of x is 65.
Find x.
Therefore, the value of X is 70.
Find x.
Therefore, the value of X is 70.
