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
The distance between parallel sides of a trapezium is 15 cm and the length of the line segment joining the mid-points of its non-parallel sides is 26 cm. Find the area of the trapezium.
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 perimeter of a rectangular board is 70 cm. Taking its length as x cm, find its width in terms of x.
If the area of the rectangular board is 300 cm2; find its dimensions.
How many tiles, each of area 400 cm2, will be needed to pave a footpath which is 2 m wide and surrounds a grass plot 25 m long and 13 m wide?
The following diagram shows a pentagonal field ABCDE in which the lengths of AF, FG, GH, and HD are 50 m, 40 m, 15 m and 25 m, respectively, and the lengths of perpendiculars BF, CH and EG are 50 m, 25 m and 60 m respectively. Determine the area of the field.
The diagram, given below, shows two paths drawn inside a rectangular field 80 m long and 45 m wide. The widths of the two paths are 8 m and 15 m as shown. Find the area of the shaded portion.
Find the area and perimeter of a square plot of land, the length of whose diagonal is 15 meters. Given your answer correct to 2 places of decimals.
Find the diagonal of a quadrilateral whose area is 756cm2 and the perpendicular from the opposite vertices are 17cm and 19cm.
When proving that a quadrilateral is a parallelogram by using slopes you must find
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.
