Area of various geometric shapes

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.

1. Use the letters of the shape to identify which parts it contains.
2. Add the required parts, or subtract the parts outside the shape from the area of the whole square.

Circle area is S = π × r². First multiply the radius by itself, then multiply by 3.14. Round only the final result to the nearest integer; round up if the tenths digit is at least 5.

A sector is part of a circular region. Its fraction of the total area equals its central angle as a fraction of a full turn.

1. Use the sector name to identify its bounding radii. Count the equal small sectors inside the required sector and the total number in the circle.
2. Find the area of the whole circle: A = π · r². Use the radius given in the question, not a length measured from the drawing.
3. Multiply the whole area by the required fraction: A_sector = π · r² · m / N, where m is the number of parts in the required sector and N is the total number of equal parts.
4. If the central angle α is known, the same fraction is α / 360°.

Use π = 3.14 in this question. Round only the final sector area to the nearest whole number, not intermediate calculations.

Rectangle area = length × width. Multiply the two side lengths. If they are in centimetres, express the result in square centimetres, cm².

The full rectangle has width AB = AE + EB and height AD, so its area is (AE + EB) × AD. Triangle areas AED and CEB are AE × AD ÷ 2 and EB × AD ÷ 2. Identify the requested region by its vertices, then subtract excluded triangles from the full area or add the required parts.

Triangle area = base × perpendicular height ÷ 2. Multiply the base by the height, then divide by 2. Express the result in cm².

Find each rectangle area separately: a × b and c × d. Since they do not overlap, the total area is the sum of the two areas. Use cm².

Circle area is S = π × r². First multiply the radius by itself, then multiply by 3.14. Round only the final result to the nearest integer; round up if the tenths digit is at least 5.

Find each rectangle area separately: a × b and c × d. Since they do not overlap, the total area is the sum of the two areas. Use cm².