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In the triangle PQR, T, U and V are the mid points of the sides PQ, PR and QR. If \( ar (TUVQ) = k \times ar (PTU) \) then what is the value of \( k \)?
The areas of the triangle PTU is equal to the area of the triangle TUV because PTVU is a parallelogram. Similarly the area of the triangle TUV is equal to the area of the triangle TQV because QTUV is a parallelogram. Therefore, the area of parallelogram TUVQ is 2 times the area of the triangle PTU. Therefore, .
In the triangle PQR, T, divides the line QR in the ratio 2:7. What is the area of the triangle PQT?
(1)
In the parallelogram PQRS, ST is perpendicular to PQ and SU is perpendicular to QR. If PQ = 15, PS = 12 and ST = 10, what is the length of SU?
Area of a parallelogram is base times the corresponding altitude.
(1)
In the parallelogram PQRS, K is the midpoint of side PQ. If the area of PKRS is 33 square inches, then what is the area of the triangle SKR?
Area of triangle PKS is onefourth of the area of the parallelogram and onethird of the area of the quadrilateral PKRS.
(1)
In the triangle PQR, QR = 6 and PR = 5. PT is perpendicular to QR and QU is perpendicular to PR. If the length of PT is 4 then what is the length of QU?
Area of triangle is half times the product of base and corresponding altitude.
(1)
What is the area of the parallelogram given below?
Area of a parallelogram is the product of base and corresponding altitude. and FG = EF. Therefore, .
In the triangle PQR, T, U and V are the mid points of the sides PQ, PR and QR. If the area of triangle TUV is 18 square feet then what is the area of the triangle PQR?
The areas of the triangle TUV is equal to the area of the triangle PTU because PTVU is a parallelogram. Similarly the area of the triangle TUV is equal to the area of the triangle TQV because QTUV is a parallelogram. Similarly the area of the triangle TUV is equal to the area of the triangle UVR because TURV is a parallelogram. Therefore, the area of triangle PQR is 4 times the area of the triangle PTU. Therefore, square feet.
In the triangle PQR, PK is the median on the side QR. If the area of triangle PQR is 36 square feet then what is the area of the triangle PQK?
Median divides a triangle into two triangles of equal areas. Area of triangle PQR is 36 square feet. Therefore, the area of the triangle PQK is 18 square feet.
In the triangle PQR, PK is the median on the side QR and QL is the median on the side PK. If the area of triangle PQR is 48 square feet then what is the area of the triangle PQL?
Median divides a triangle into two triangles of equal areas. Area of triangle PQR is 48 square feet. Therefore, the area of the triangle PQK is 24 square feet and the area of the triangle PQL is 12 square feet.
The figure EFGH is a parallelogram. If the area of the triangle EFK is 15 and the area of the triangle HGK is 27, then what is the area of the parallelogram EFGH?
Sum of areas of triangles EFK and HGK is equal to the area of the triangle EKH. Therefore, area of triangle EKH is 42. Therefore, the area of the parallelogram EFGH is 84.
Which of the following figures is formed by joining the midpoints of a rectangles having adjacent sides as 18 and 10?
The figure formed by joining the mid points of rectangle has equal sides. So it is a rhombus and it has the area equal to half the area of the rectangle. So it is a rhombus of area 90.
EFGH is a trapezium having EH parallel to FG and the line MN is formed by joining the midpoints of lines EF and HG. If \( FG = p \) and \( EH = q \), then what is the ratio of the ar EHNM and ar FGNM?
Altitude of the trapeziums EHNM and FGNM are equal.
(1)
Therefore, the required ratio is
(2)
Which of the following statement is correct?
Correct statement is median of a triangle divides it in two triangles of equal areas.
In the following parallelogram PQRS, K is the midpoint of SR. If the area of the parallelogram PQRS is 64 square inches then what is the area of the triangle KSQ?
Area of triangle is half of the area of the parallelogram. Therefore, the area of the triangle RSQ is 32 square inches. Median of a triangle divides the triangle in two triangles of equal areas. KQ is the median on the side SR. Therefore, the area of the triangle KSQ is 16 square inches.