Advertisements
Advertisements
Question
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)
Solution
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
RELATED QUESTIONS
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.
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.
The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If the area of the rectangle is three times the area of the square; find the dimensions of each.
Trapezium given below; find its area.
The width of a rectangular room is `4/7`of its length, x, and its perimeter is y. Write an equation connecting x and y. Find the length of the room when the perimeter is 4400 cm.
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm; find the distance between the shorter sides.
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?
Find the area of a quadrilateral field whose sides are 12m, 9m, 18m and 21m respectively and the angle between the first two sides is a right angle. Take the value of `sqrt(6)` as 2.5.
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (0, 0), (p, 8), (6, 2) | 20 |
The quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of the patio
