Advertisements
Advertisements
Question
The quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of the patio
Advertisements
Solution
Area of the Quadrilateral ABCD = `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)]`
= `1/2[(16 + 80 + 36 + 80) - (-64 - 24 - 100 - 24)]`
= `1/2[212 - (-212)]`
= `1/2[212 + 212]`
= `1/2[424]`
= 212 sq. units
Area of the Quadrilatera swimming pool EFGH = `1/2[(6 + 42 + 12 + 30) - (- 30 - 6 - 42 - 12)]`
= `1/2[90 - (- 90)]`
= `1/2[90 + 90]`
= `1/2 xx 180`
= 90 sq. units
Area of the patio = Area of the Quadrilateral ABCD – Area of the Quadrilateral EFGH
= (212 – 90) sq. units
Area of the patio = 122 sq. units
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.
The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.
A rectangular plot of land measures 45 m x 30 m. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.
Trapezium given below; find its area.
A wire when bent in the form of a square encloses an area of 484 m2. Find the largest area enclosed by the same wire when bent to from:
- An equilateral triangle.
- A rectangle of length 16 m.
Calculate the area of the figure given below:
Which is not drawn scale.
The length of a rectangular verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x as the breadth of the verandah, write an equation in x that represents the above statement
(ii) Solve the equation obtained in (i) above and hence find the dimensions of the verandah.
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.
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 area of the quadrilateral whose vertices are at (– 9, – 2), (– 8, – 4), (2, 2) and (1, – 3)
