Test
Area of various geometric shapes
This test develops area calculations for rectangles, triangles, circles, trapezoids and other geometric figures. Tasks require students to choose an appropriate formula, substitute dimensions correctly and give answers in square units.
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Question 1out of 10
In the diagram, a square ABCD is depicted. The length of the side is 12. Find the area of the shape DEFC.
First find the area of the whole square by multiplying its side length by itself.
The diagonals divide the square into four triangles of equal area, so each has one quarter of the square area. The segment from the intersection of the diagonals to the midpoint of a side divides one of those triangles in half, so each small triangle has one eighth of the square area.
- Use the letters of the shape to identify which parts it contains.
- Add the required parts, or subtract the parts outside the shape from the area of the whole square.
Question 2out of 10
Question 3out of 10
Find the area of the circle.
The radius of the circle is 15.
Use the constant π as 3.14.
Round the result to the nearest integer.
Question 4out of 10
Question 5out of 10
Find the area of the shape AED, where segment AE is 8, segment EB is 4, and AD is 4.
Question 6out of 10
Find the area of the circle.
The radius of the circle is 10.
Use the constant π as 3.14.
Round the result to the nearest integer.
Question 7out of 10
In the diagram, a square ABCD is depicted. The length of the side is 8. Find the area of the shape ABEFCD.
First find the area of the whole square by multiplying its side length by itself.
The diagonals divide the square into four triangles of equal area, so each has one quarter of the square area. The segment from the intersection of the diagonals to the midpoint of a side divides one of those triangles in half, so each small triangle has one eighth of the square area.
- Use the letters of the shape to identify which parts it contains.
- Add the required parts, or subtract the parts outside the shape from the area of the whole square.
Question 8out of 10
Find the area of the sector AOD of a circle.
The radius of the circle is 19.
Use the constant π as 3.14.
Round the result to the nearest integer.
Question 9out of 10
Question 10out of 10
Calculate the area of the shape ABD.
Time left: 00:00:00
Sample questions
- In the diagram, a square ABCD is depicted. The length of the side is ___. Find the area of the shape ___.
- Calculate the area of the shape ___.
- Find the area of the sector ___ of a circle. The radius of the circle is ___. Use the constant π as 3.14. Round the result to the nearest integer.
- Find the area of the circle. The radius of the circle is ___. Use the constant π as 3.14. Round the result to the nearest integer.
- Find the area of the shape ___, where segment AE is ___, segment EB is ___, and AD is ___.
Areas of geometric figures
Area is measured in square units. For a rectangle A = ab, triangle A = ah/2, parallelogram A = ah, trapezoid A = (a + b)h/2 and circle A = πr².
Composite shapes
Divide a composite shape into simpler parts and add their areas, or subtract a missing part from a larger shape. Convert all lengths to the same unit before applying a formula.
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