Class 10
Abcd is a trapezium AB||CD
Area related to circles
Answers
Given that,
A trapezium ABCD in which AB || CD such that
AO = x - 1
CO = BO = x + 1
OD = x + 4
Now,
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
SHORT CUT TRICK
The diagonals of the trapezium divides each other proportionally. i.e. If ABCD is a trapezium and diagonals AC and BD intersects at O, then
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
LEARN MORE
1. Pythagoras Theorem :-
This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.
2. Converse of Pythagoras Theorem :-
This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.
3. Area Ratio Theorem :-
This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.
4. Basic Proportionality Theorem :-
This theorem states that :- If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.
Step-by-step explanation:
AB=7cm,DE=4cm,BF=3.5cm
BC=DE+EC=(4+7)cm=11cm
Area pf trapezium ABCD=
2
1
×(Sum of parallelogram)×(Distance between them)
=
2
1
×(11+7)×3.5
=
2
1
×18×3.5
=31.5cm
2
Area of the sector BGEC=
360
30
×
9
22
×7×7
=
12
1
×22×7
=12.83cm
2
Area of shaded region = Area of trapezium - Arc of sector
(31.5−12.88)cm
2
=18.67cm
2