# Area of shape + ratio - math problems

Area is the quantity that expresses the extent of a two-dimensional shape. The area can be understood as the amount of paint necessary to cover the surface with a single coat. The area of a shape can be measured by comparing the shape to squares of a fixed size 1 m^2 or 1 cm^2 etc. Every unit of length has a corresponding unit of area. Areas can be measured in square metres (m^2), square centimetres (cm^2), square millimetres (mm^2), square kilometres (km^2), square feet (ft^2), square yards (yd^2), square miles (mi^2), and so forth.

#### Number of problems found: 81

• Ratio of sides 2 The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.
• In the In the national park, the ratio of the wooded area to grassland is 4: 1. The total area is 385km2. What area is wooded?
• Square to rectangle What is the ratio of the area of a square of side x to the area of a rectangle of a rectangle of width 2 x and length 3
• Rectangle - sides ratio Calculate the area of a rectangle whose sides are in ratio 3:13 and perimeter is 673.
• Divide Divide area of rectangles with dimensions 32m and 10m by the ratio 7: 9. What area corresponds to a smaller section?
• Pipeline How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
• The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
• Rectangle area The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
• Ratio - rectangle The rectangle has dimensions 6 cm and 9 cm. How many times increases area and its perimeter, when its dimensions increase in the ratio 5:3?
• Two gardeners The garden with an area of 81 square meters was divided by two gardeners in a ratio of 4: 5. How much did the second gardener get more first?
• Ratio of volumes If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
• Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
• Similarity of squares The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?
• Axial section The axial section of the cylinder has a diagonal 31 cm long, and we know that the area of the side and the base area is in ratio 3:2. Calculate the height and radius of the cylinder base.
• Three shapes 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
• MO Z9–I–2 - 2017 In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.
• Trapezoid - diagonal A trapezoid has a length of diagonal AC crossed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
• Ratio of sides Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• Trapezoid - central median The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
• Rhombus and diagonals The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.

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