# Area of shape - 9th grade (14y) - 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: 417

• Regular triangular pyramid Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
• Compute 4 Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
• Rectangular garden The perimeter of Peter's rectangular garden is 98 meters. The width of the garden is 60% shorter than its length. Find the dimensions of the rectangular garden in meters. Find the garden area in square meters.
• Triangle Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
• Two lands The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
• Triangular pyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
• Rectangle The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
• Hexagonal pyramid Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
• Center of gravity In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
• Map scale On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters?
• Isosceles trapezoid In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
• Diagonal he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
• Mice Mice consumed a circular hole in a slice of cheese. The cheese has the shape of a circular cut with a radius of 20 cm and an angle of 90 degrees. What percentage of the cheese ate mice if they made 20 holes with a diameter of 2 cm?
• Right triangle Calculate the missing side b and interior angles, perimeter, and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
• Logs The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
• Tetrahedral pyramid Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm2, and the deviation angle of the side edges from the plane of the base is 60 degrees.
• The regular The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
• Isosceles trapezoid The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
• Trapezoid MO-5-Z8 ABCD is a trapezoid that lime segment CE is divided into a triangle and parallelogram, as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE, and the area of the triangle CDE is 3 cm2. Determine the area of the trape
• Diagonal intersect isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...