Advertisements
Advertisements
प्रश्न
In the figure, PT is parallel to SR. QTSR is a parallelogram and PQSR is a rectangle. If the area of ΔQTS is 60cm2, find:
(i) the area o || gm QTSR
(ii) the area of the rectangle PQRS
(iii) the area of the triangle PQS.
उत्तर
(i) ar(ΔQTS) = `(1)/(2)` x ar(parallelogram QTSR)
(The area of a triangle is half that of a parallelogram on the same base and between the same parallels)
⇒ ar(parallelogram QTSR) = 2 x ar(ΔQTS)
⇒ ar(parallelogram QTSR) = 2 x 60cm2
⇒ ar(parallelogram QTSR) = 120cm2
(ii) ar(ΔQTS) = `(1)/(2)` x ar(parallelogram QTSR)
ar(ΔQTS) = ar(ΔRSQ) = 60cm2
Now,
ar(ΔRSQ) = `(1)/(2)` x ar(rectangle PQRS)
⇒ ar(rectangle PQRS) = 2 x ar(ΔRSQ)
⇒ ar(rectangle PQRS) = 2 x 60cm2
⇒ ar(rectangle PQRS) = 120cm2
(iii) Since PQRS is a rectangle,
Therefore RS = PQ .....(i)
QTSR is a parallelogram,
Therefore, RS = QT .....(ii)
From (i) and (ii)
PQ = QT .......(iii)
In ΔPSQ and ΔQST
QS = QS
PQ = QT ...(from (iii))
∠PQS = ∠SQT = 90°
Therefore, ΔPSQ ≅ ΔQST
Area of two congruent triangles is equal.
Hence, ar(ΔPSQ) = ar(ΔQTS) = 60cm2.
APPEARS IN
संबंधित प्रश्न
State, 'true' or 'false'
Every parallelogram is a rhombus.
State, 'true' or 'false'
If the diagonals of a quadrilateral bisect each other at right angle, the quadrilateral is a square.
In the following figures, ABCD is a parallelogram.
Find the values of x and y.
In the given figure ABCD is a rhombus with angle A = 67°
If DEC is an equilateral triangle, calculate:
- ∠CBE
- ∠DBE
In the figure, ABCD is a parallelogram and APD is an equilateral triangle of side 80cm, Calculate the area of parallelogram ABCD.
In the figure, PQR is a straight line. SQ is parallel to Tp. Prove that the quadrilateral PQST is equal in area to the ΔPSR.
The diagonals of a parallelogram ABCD intersect at O. A line through O meets AB in P and CD in Q. Show that
(a) Area of APQD = `(1)/(2)` area of || gm ABCD
(b) Area of APQD = Area of BPQC
If the medians of a ΔABBC intersect at G, show that ar(ΔAGB) = ar(ΔAGC) = ar(ΔBGC) = `(1)/(3)"ar(ΔABC)"`.
Two adjacent sides of a parallelogram are 20cm and 18cm. If the distance between the larger sides is 9cm, find the area of the parallelogram. Also, find the distance between the shorter sides.
In a trapezium the parallel sides are 12cm and 8cm. If the distance between them is 6cm, find the area of the trapezium.
A rectangular floor 45 in long and 12 m broad is to be paved exactly with square tiles, of side 60 cm. Find the total number of tiles required to pave it.
If a carpet is laid on the floor such as a space of 50 cm exists between its edges and the edges of the floor, find what fraction of the floor is uncovered.
The area of a square garden is equal to the area of a rectangular plot of length 160m and width 40m. Calculate the cost of fencing the square garden at Rs.12per m.
Find the perimeter and area of a square whose diagonal is `5sqrt(2)"cm"`. Give your answer correct to two decimal places if `sqrt(2)` = 1.414.
The area of a rhombus is 234 cm2. If its one diagonal is 18 cm, find the lengths of its side and the other diagonal. Also, find perimeter of the rhombus.
A lawn in the shape of a rectangle is to be developed in front of a Marriage Hall. The length and breadth of the lawn are 44m and 32m. A space of 2m is left on the two shoulder sides and one longer side for flower and in the remaining area grass is laid. Calculate the area of the flower space and the area on which grass is laid.
A rectangular field is 240m long and 180m broad. In one corner a farm house is built on a square plot of side 40m. Find the area of the remaining portion and the cost of fencing the open sides Rs.25per m.
The length and breadth of a rectangular field are in the ratio 8 : 5. A 2m wide path runs all around outside the field. The area of the path is 848m2. Find the length and breadth of the field.
Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.
The opposite sides of a trapezium are parallel.
Name polygon.
Make two more examples of this.
