Advertisements
Advertisements
प्रश्न
Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are (– 4, – 2), (– 3, k), (3, – 2) and (2, 3)
Advertisements
उत्तर
Let the vertices A(– 4, – 2), B(– 3, k), C(3, – 2) and D(2, 3)
Area of the Quadrilateral = 28 sq. units
`1/2[(x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1) - (x_2y_1 + x_3y_2 + x_4y_3 + x_1y_4)]` = 28
`1/2[(-4"k" + 6 + 9 - 4) - (6 + 3"k" - 4 - 12)]` = 28
`1/2[(-4"k" + 11) - (3"k" - 10)]` = 28
– 4k + 11 – 3k + 10 = 56
– 7k + 21 = 56
– 7k = 56 – 21
– 7k = 35
⇒ 7k = – 35
k = `35/7`
= – 5
The value of k = – 5
APPEARS IN
संबंधित प्रश्न
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
The area of a parallelogram is y cm2 and its height is h cm. The base of another parallelogram is x cm more than the base of the first parallelogram and its area is twice the area of the first. Find, in terms of y, h, and x, the expression for the height of the second parallelogram.
A wire when bent in the form of a square encloses an area = 576 cm2. Find the largest area enclosed by the same wire when bent to form;
(i) an equilateral triangle.
(ii) A rectangle whose adjacent sides differ by 4 cm.
Trapezium given below; find its area.
The area of a rhombus is 216 sq. cm. If it's one diagonal is 24 cm; find:
(i) Length of its other diagonal,
(ii) Length of its side,
(iii) The perimeter of the rhombus.
The rate for a 1.20 m wide carpet is Rs. 40 per meter; find the cost of covering a hall 45 m long and 32 m wide with this carpet. Also, find the cost of carpeting the same hall if the carpet, 80 wide, is at Rs. 25. Per meter.
A floor that measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 25 cm. Find the number of tiles required.
Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges and the edges of the floor, what fraction of the floor is left uncovered?
Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.
Find the area and the perimeter of a square with diagonal 24 cm. [Take √2 = 1.41 ]
PQRS is a rectangle formed by joining the points P(– 1, – 1), Q(– 1, 4), R(5, 4) and S(5, – 1). A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.
